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During the last two decades, the decentralized execution of business processes has been one of the main research topics in Business Process Management. Several models (languages) for processes' specification in order to facilitate their distributed execution, have been proposed. LSAWfP is among the most recent in this area: it helps to specify administrative processes with grammatical models indicating, in addition to their fundamental elements, the permissions (reading, writing and execution) of each actor in relation to each of their tasks. In this paper, we present a model for a completely decentralized and artifact-centric execution of administrative processes specified using LSAWfP. The presented model puts particular emphasis on actors' views: it then allows the confidential execution of certain tasks by ensuring that, each actor potentially has only a partial perception of the processes' global execution states. The model thus solves a very important problem in business process execution, which is often sidelined in existing approaches. To accomplish this, the model rely on three projection algorithms allowing to partially replicate the processes' global execution states at a given moment, to consistently update the obtained partial states and to deduce new coherent global states. The proposal of these three algorithms, the proof of underlying mathematical tools' stability and a proposal of their implementation, are this paper's main contributions.

In this technical note, we present an adaptive fuzzy hierarchical sliding mode control method to deal with the control problem of under-actuated switched nonlinear systems. For the system under consideration, both the issues of unknown uncertain functions and aperiodically updating input are taken into account, which are of practical importance. A bounded time-varying function is employed to make a linear transformation of the control input, leading to a transformed system that can be applied to the control design. By introducing the so-called hierarchical structure, a top layer hierarchical sliding surface containing all the system states' information is obtained. Furthermore, by carrying out fuzzy logic systems' universal approximation, the problem caused by unknown system uncertainties is tackled. The approximation errors together with the measurement error resulted from the effects of the triggering event are lumped into a function, and its upper bound is estimated on-line. Based on these, the boundedness of all the signals are verified by combining the Lyapunov theory and projection algorithm. To testify the validity of our control scheme, a simulation example is carried out.

This study proposes an online-trained adaptive fuzzy-neural-network power decoupling (AFNNPD) strategy for a virtual synchronous generator (VSG) control in a micro-grid (MG). Firstly, the mechanism of the power coupling for the VSG control in a MG is analyzed, and the system dynamic model for the proposed power decoupling method is derived. Then, a total sliding-mode controller (TSMC) is designed for the power decoupling with the characteristics of the strong robustness and fast dynamic response. Moreover, an adaptive fuzzy-neural-network (AFNN) control is designed to mimic the TSMC law for relaxing the requirement of the detail system information in the TSMC. In addition, adaptive tuning laws for network parameters are derived according to the projection algorithm and the Lyapunov stability theorem for guaranteeing the network convergence as well as the totally power decoupling performance. Furthermore, experimental results are provided to verify the superiority of the proposed AFNNPD method in comparison with conventional methods.

The graph partition problem (GPP) aims at clustering the vertex set of a graph into a fixed number of disjoint subsets of given sizes such that the sum of weights of edges joining different sets is minimized. This paper investigates the quality of doubly nonnegative (DNN) relaxations, i.e., relaxations having matrix variables that are both positive semidefinite and nonnegative, strengthened by additional polyhedral cuts for two variations of the GPP: the k-equipartition and the graph bisection problem. After reducing the size of the relaxations by facial reduction, we solve them by a cutting-plane algorithm that combines an augmented Lagrangian method with Dykstra's projection algorithm. Since many components of our algorithm are general, the algorithm is suitable for solving various DNN relaxations with a large number of cutting planes. We are the first to show the power of DNN relaxations with additional cutting planes for the GPP on large benchmark instances up to 1,024 vertices. Computational results show impressive improvements in strengthened DNN bounds.

Compressed sensing (CS) aims to reconstruct a high quality images with as little sample data as possible. Magnetic resonance imaging (MRI) plays an important role in medical imaging tools but has a slower data acquisition process. Applying CS to MRI offers significant scan time reductions. In this paper, we proposed a fast and efficient algorithm for compressed sensing magnetic resonance imaging (CS-MRI) reconstruction, denoted as adjustable shrinkage-thresholding projection algorithm (ASTP). It is designed to use adjustable shrinkage rules for lp-norm based CS-MRI model. This algorithm is established by using an iterative projection and acceleration scheme. In each iteration, the proposed adjustable shrinkage-thresholding rules are employed to ensure global convergence to accurate solution. Furthermore, the parameter p can be selected flexibly according to different practical application situations, and the orthogonal projection operation is used to reduce the dimension of the solution space to accelerate the convergence speed and improve the reconstruction quality. Numerical experiments show that proposed ASTP algorithm provides a higher accuracy, convergence speed and ability to suppress noise compared with some certain state-of-the-art algorithms.

In this letter, we propose a novel method to find matrices that satisfy sparsity and LMI (linear matrix inequality) constraints at the same time. This problem appears in sparse control design such as sparse representation of the state feedback gain, sparse graph representation with fastest mixing, and sparse FIR (finite impulse response) filter design, to name a few. We propose an efficient algorithm for the solution based on Dykstra’s projection algorithm. We then prove a convergence theorem of the proposed algorithm, and show some control examples to illustrate merits and demerits of the proposed method.

This paper proposes a multistage robust optimization model for distribution system operation with energy storage under uncertainty. Unlike the conventional robust optimization paradigm which minimizes the worst-case cost, the proposed formulation optimizes the cost in the nominal scenario. In analogy to dynamic programming, we define dynamic robust feasible regions in a recursive manner. In each period, the dynamic robust feasible region is shown to be polyhedral, and a linear programming based projection algorithm is developed to compute such regions offline. In the online stage, the method is executed following a rolling horizon manner: renewable output is observed at the beginning of each period, and the cost of remaining periods in the forecast scenario is to be minimized subject to operation constraints and dynamic robust feasible regions, giving rise to a linear program. In this way, the dispatch strategy ensures multistage operation security regardless of future realizations of renewable power. In numeric tests on a modified IEEE 33-bus distribution system, the dynamic robust feasible regions are visualized and analyzed, and the proposed method is compared with two prevailing robust optimization methods, verifying its advantages in terms of optimality and robustness

This paper presents a novel variational model based on fuzzy clustering and total variation regularization for superpixel segmentation. Compared with the classical hard-labeled methodologies, our approach gives soft results via the fuzzy membership function, and moreover, the use of total variation provides additional information that can enhance the superpixel regularity, which in turn improves the segmentation performance. To efficiently minimize the energy functional of the proposed model, we adopt an alternating direction method of multipliers with the modified Chambolle's fast duality projection algorithm. Our algorithm can generate regular and compact superpixels with high segmentation accuracy, satisfactory boundary adherence and low computational cost. Comparative experimental results with the current state-of-the-art approaches reveal the superior performance of the proposed method.

This paper studies the distributed convex optimization problem with a common decision variable, a global inequality constraint, and local constraint sets over a time-varying multi-agent network, the objective function of which is a sum of agents' local convex cost functions. To solve such problem, a penalty-based distributed continuous-time subgradient algorithm with time-varying gain is developed for each agent to seek the saddle point of the penalty Lagrangian function. It is shown that an exact primal optimal solution can be obtained with certain assumption on time-varying gain. Moreover, the proposed algorithm adopts fixed-time projection scheme to ensure that for any initial state value, each local state estimate converges to its convex constraint set within fixed time. Finally, numerical examples are provided to show the effectiveness of the theoretical results.

In this paper we suggest a theoretical framework to study the generalized split null point problem (GSNPP) via a multi-step inertial based parallel hybrid projection algorithm in Hilbert spaces. The architecture and the suitable set of control conditions ensure the strong convergence of the algorithm. The possible applications of the algorithm are illustrated via various theoretical and numerical results. The key advantages of the algorithm are highlighted in comparison to the classical and non-inertial algorithm as well as (one-step and two-step) inertial variants of the algorithm for the GSNPP.

In this article, we study the recursive algorithms for a class of separable nonlinear models (SNLMs) in which the parameters can be partitioned into a linear part and a nonlinear part. Such models are very common in machine learning, system identification, and signal processing. Utilizing the special structure of the SNLMs, we propose a recursive variable projection (RVP) algorithm, in which at each recursion, the linear parameters of the model are eliminated, and the nonlinear parameters are updated by the recursive Levenberg-Marquart algorithm. Then, based on the updated nonlinear parameters, the linear parameters are updated by the recursive least-squares algorithm. According to a convergence analysis of the RVP algorithm, the parameter estimation error is mean-square bounded. Numerical examples confirm the satisfactory performance of the proposed algorithm.

In this paper, by combining the Solodov and Svaiter projection technique with the conjugate gradient method for unconstrained optimization proposed by Mohamed et al. (2020), we develop a derivative-free conjugate gradient method to solve nonlinear equations with convex constraints. The proposed method involves a spectral parameter which satisfies the sufficient descent condition. The global convergence is proved under the assumption that the underlying mapping is Lipschitz continuous and satisfies a weaker monotonicity condition. Numerical experiment shows that the proposed method is efficient.

This paper deals with the convergence analysis of a shrinking approximants for the computation of a common solution associated with the fixed point problem of $$\eta $$ -demimetric operator and the generalized split null point problem in Hilbert spaces. The considered sequence of approximants is a variant of the parallel hybrid shrinking projection algorithm that converges strongly to the optimal common solution under suitable set of control conditions. The viability of the approximants with parallel implementation is demonstrated for various theoretical as well as numerical results. The results presented in this paper improve various existing results in the current literature.

In this paper, we introduce a new inertial subgradient projection algorithm for finding a solution of an equilibrium problem in a real Hilbert space. The algorithm combines subgradient projection methods with the self-adaptive and inertial techniques to generate an iteration sequence converging weakly to a solution of the equilibrium problem. Based on the proposed algorithm, we develop a modified algorithm for finding a common solution of the equilibrium problem and fixed point problems. Several of fundamental experiments are showed to illustrate our algorithms and compare with some others.

This paper investigates a distributed recursive projection identification problem with binary-valued observations built on a sensor network, where each sensor in the sensor network measures partial information of the unknown parameter only, but each sensor is allowed to communicate with its neighbors. A distributed recursive projection algorithm is proposed based on a specific projection operator and a diffusion strategy. The authors establish the upper bound of the accumulated regrets of the adaptive predictor without any requirement of excitation conditions. Moreover, the convergence of the algorithm is given under the bounded cooperative excitation condition, which is more general than the previously imposed independence or persistent excitations on the system regressors and maybe the weakest one under binary observations. A numerical example is supplied to demonstrate the theoretical results and the cooperative effect of the sensors, which shows that the whole network can still fulfill the estimation task through exchanging information between sensors even if any individual sensor cannot.

We study the quadratic cycle cover problem (QCCP), which aims to find a node-disjoint cycle cover in a directed graph with minimum interaction cost between successive arcs. We derive several semidefinite programming (SDP) relaxations and use facial reduction to make these strictly feasible. We investigate a nontrivial relationship between the transformation matrix used in the reduction and the structure of the graph, which is exploited in an efficient algorithm that constructs this matrix for any instance of the problem. To solve our relaxations, we propose an algorithm that incorporates an augmented Lagrangian method into a cutting-plane framework by utilizing Dykstra’s projection algorithm. Our algorithm is suitable for solving SDP relaxations with a large number of cutting-planes. Computational results show that our SDP bounds and efficient cutting-plane algorithm outperform other QCCP bounding approaches from the literature. Finally, we provide several SDP-based upper bounding techniques, among which is a sequential Q-learning method that exploits a solution of our SDP relaxation within a reinforcement learning environment. Summary of Contribution: The quadratic cycle cover problem (QCCP) is the problem of finding a set of node-disjoint cycles covering all the nodes in a graph such that the total interaction cost between successive arcs is minimized. The QCCP has applications in many fields, among which are robotics, transportation, energy distribution networks, and automatic inspection. Besides this, the problem has a high theoretical relevance because of its close connection to the quadratic traveling salesman problem (QTSP). The QTSP has several applications, for example, in bioinformatics, and is considered to be among the most difficult combinatorial optimization problems nowadays. After removing the subtour elimination constraints, the QTSP boils down to the QCCP. Hence, an in-depth study of the QCCP also contributes to the construction of strong bounds for the QTSP. In this paper, we study the application of semidefinite programming (SDP) to obtain strong bounds for the QCCP. Our strongest SDP relaxation is very hard to solve by any SDP solver because of the large number of involved cutting-planes. Because of that, we propose a new approach in which an augmented Lagrangian method is incorporated into a cutting-plane framework by utilizing Dykstra’s projection algorithm. We emphasize an efficient implementation of the method and perform an extensive computational study. This study shows that our method is able to handle a large number of cuts and that the resulting bounds are currently the best QCCP bounds in the literature. We also introduce several upper bounding techniques, among which is a distributed reinforcement learning algorithm that exploits our SDP relaxations.

In the blade computer numerical control (CNC) machining process, the machining fixture design for each type of blade will be a very difficult task due to the large variety and quantity of blades. This study proposes a computer-aided machining fixture design algorithm and software based on case learning. The three-dimensional model of the case learning blade and the target blade is firstly projected into a cylinder surface based on the projection algorithm, and the cylinder surface is expanded into a two-dimensional plane based on expansion algorithm. Then, the matching machining fixture layout of the target blade relative to the case learning blade is obtained in two-dimensional space by the mesh affine transformation algorithm according to the geometric edge constraints and the matching relationship of the case learning blade and target blade. At last, the inverse transformations of projection and expansion are used to obtain the final fixture layout of the target blade three-dimensional model based on the previous projection and expansion relationship. The special computer-aided fixture design software of near-net shaped blade is developed, and the machining fixture design and CNC machining experiment based on two typical near-net-shaped blades proved that the computer-aided fixture design algorithm based on case learning is feasible and can be used to realize the intelligent design of near-net-shaped blade machining fixture.

Chronic Kidney disease is one of the eminent diseases which is commonly seen the patients which the various ailments which results in the step by step failure of kidneys which may result in the fatality of the human. The Chronic Kidney disease which is precisely called as CKD in medical terms is predicted with various symptoms that evolves in the human body. Strategically predicting the CKD using the machine learning algorithm is the challenging proportion. This paper solves the issues of predicting the CKD using the Hierarchical Decision-Tree Projection Algorithm which takes the various clinical study results of the human body into the dataset format and is algorithmically evaluated. Through this method the whole study in completely evaluated with the various parameters which is obtained from the human study. The variations in the whole study with respect to the parametrical correlation are taken into consideration. The results are obtained from each parametrical evaluation and with the results the prediction and presence of the Chronic Kidney disease is evaluated. The Experimental results show the algorithmic evaluations are showing the comparatively high accuracy and performance.

In this paper, we propose an incremental constraint projection method (i.e., random or cyclic projection algorithm) for solving variational inequality problem with special structure, which the underlying mapping is strongly monotone and the constraint set is the intersection of a large number of simple closed convex sets. Compared with some existing projection type algorithms, the proposed method has two notable advantages: Its global convergence can be guaranteed without the Lischitz continuity of underlying mapping in almost sure sense; It just computes only one halfspace projection rather than the projection of the full or single constraint set at each iteration. Preliminary computational experience is also reported to illustrate the effectiveness of the proposed method.

Spinal pathology treatment has become an urgent issue to be solved. How to effectively prevent and treat spinal pathology has become a research hotspot in the field of surgery. Aiming at the problem of too long volume rendering time caused by the trilinear interpolation sampling method in the reconstruction and visualization of the vertebra 3D model, an improved ray projection algorithm is proposed to quickly reconstruct a 3D vertebra model from medical CT vertebra images. This method first classifies CT data, assigns corresponding color values and opacity transfer functions to different types of data, and then uses inverse distance-weighted interpolation (IDWI) sampling to replace the trilinear interpolation sampling method for the voxel where the sampling point is located to accelerate the interpolation operation. The color value and opacity of the sampling points are obtained, and finally, the attributes of all the sampling points are synthesized and calculated to obtain the final rendering effect, and the reconstruction of the three-dimensional vertebra model is completed. Experimental results show that the proposed method not only can obtain higher quality rendered images but also has a certain improvement in rendering speed compared with traditional algorithms.

It is well known that the monotonicity of the underlying mapping of variational inequalities plays a central role in the convergence analysis. In this paper, we propose an infeasible projection algorithm (IPA for short) for nonmonotone variational inequalities. The next iteration point of IPA is generated by projecting a vector onto a half-space. Hence, the computational cost of computing the next iteration point of IPA is much less than the algorithm of Ye and He (Comput. Optim. Appl. 60, 141–150, 2015) (YH for short). Moreover, if the underlying mapping is Lipschitz continuous with its modulus is known, by taking suitable parameters, IPA requires only one projection onto the feasible set per iteration. The global convergence of IPA is obtained when the solution set of its dual variational inequalities is nonempty. Moreover, if in addition error bound holds, the convergence rate of IPA is Q-linear. IPA can be used for a class of quasimonotone variational inequality problems and a class of quasiconvex minimization problems. Comparing with YH and Algorithm 2 in Deng, Hu and Fang (Numer. Algor. 86, 191–221, 2021) (DHF for short) by solving high-dimensional nonmonotone variational inequalities, numerical experiments show that IPA is much more efficient than YH and DHF from CPU time point of view. Moreover, IPA is less dependent on the initial value than YH and DHF.

Passengers traveling on transit networks involve two kinds of decision-making strategies: deciding which lines are attractive at an origin or transfer node (denoted line strategy, LS), or deciding which node to transfer at when riding a line (denoted node strategy, NS). Combining these two strategies, this paper proposes a novel variational inequality formulation for the user equilibrium passenger assignment problem. The inclusion of the NS eliminates the need for passenger assignment on a large augmented graph, reducing the modeling complexity and making it easier to track all passengers’ travel routes. Moreover, constraints on the maximal number of transfers—which are crucial in practical decision-making on transit networks—are explicitly included, further drastically reducing the set of passengers’ feasible strategies. Furthermore, some extant strategy-based transit assignment models are shown to be a special case of the proposed model when the transfer constraint is removed. Finally, the properties of the proposed model are illustrated on a small network, and the model and algorithm exhibit huge advantages on the chosen transit subnetwork of Beijing.

We study variational inequalities and fixed point problems in real Hilbert spaces. A new algorithm is proposed for finding a common element of the solution set of a pseudo-monotone variational inequality and the fixed point set of a demicontractive mapping. The advantage of our algorithm is that it does not require prior information regarding the Lipschitz constant of the variational inequality operator and that it only computes one projection onto the feasible set per iteration. In addition, we do not need the sequential weak continuity of the variational inequality operator in order to establish our strong convergence theorem. Next, we also obtain an R-linear convergence rate for a related relaxed inertial gradient method under strong pseudo-monotonicity and Lipschitz continuity assumptions on the variational inequality operator. Finally, we present several numerical examples which illustrate the performance and the effectiveness of our algorithm.

Application of near-infrared spectroscopy to the prediction of sample content is strongly limited by signal peak overlap. To analyze the spectral information directly related to the target components and to make the chemometric model more explanatory, an independent characteristic projection algorithm is proposed. The algorithm was applied to the independent spectral analysis of a single sample using corn as a representative example. Moisture, oil, protein, and starch, which are the four main components of corn, were the target components. The pure component spectra were used the projection directions to decompose the near-infrared spectrum of a single corn sample; then four decomposed spectra corresponding to the four pure component spectra were obtained. Their corresponding relationship was determined using their correlation coefficients and by comparing their characteristic peaks, and the molecular absorption patterns corresponding to the characteristic absorption peaks of each decomposed spectrum were analyzed in detail. The theoretical analysis and experimental results indicate that the independent characteristic projection algorithm can be applied to single-sample spectral analysis to extract more complete physicochemical information about the target components and provide a theoretical basis for establishing a robust near-infrared spectral chemometric model with great extrapolation capability and stability.

Temporal changes in medical images are often evaluated along a parametrized function that represents a structure of interest (e.g. white matter tracts). By attributing samples along these functions with distributions of image properties in the local neighborhood, we create distribution-valued signatures for these functions. We propose a novel, comprehensive framework which models their temporal evolution trajectories. This is achieved under the unifying scheme of Wasserstein distance metric. The regression problem is formulated as a constrained optimization problem and solved using an alternating projection algorithm. The solution simultaneously preserves the functional characteristics of the curve, models the temporal change in distribution profiles and forces the estimated distributions to be valid. Hypothesis testing is applied in two ways using Wasserstein based test statistics. Validation is presented on synthetic data. Estimation of a population trajectory is shown using diffusion properties along DTI tracts from a healthy population of infants. Detection of delayed growth is shown using a case study.

Complex 3D curves can be created by directly drawing mid-air in immersive environments (Augmented and Virtual Realities). Drawing mid-air strokes precisely on the surface of a 3D virtual object, however, is difficult; necessitating a projection of the mid-air stroke onto the user "intended" surface curve. We present the first detailed investigation of the fundamental problem of 3D stroke projection in VR. An assessment of the design requirements of real-time drawing of curves on 3D objects in VR is followed by the definition and classification of multiple techniques for 3D stroke projection. We analyze the advantages and shortcomings of these approaches both theoretically and via practical pilot testing. We then formally evaluate the two most promising techniques spraycan and mimicry with 20 users in VR. The study shows a strong qualitative and quantitative user preference for our novel stroke mimicry projection algorithm. We further illustrate the effectiveness and utility of stroke mimicry, to draw complex 3D curves on surfaces for various artistic and functional design applications., Accepted to ACM Transactions on Graphics

To improve the uniformity of coating thickness and spraying efficiency, new point cloud modeling and slicing algorithm are proposed to deal with free-form surfaces for the spray painting robot in this paper. In the process of point cloud modeling, the edge preservation algorithm is firstly presented to avoid damaging the edge characteristic of the point cloud model. For the spraying gun, the coating deposition model on the free-form surface is determined on the basis of the elliptic double β distribution model. Then, the grid projection algorithm is proposed to obtain grid points between adjacent slices on the free-form surface. Based on this, the analytical solution for calculating the coating thickness at each grid point is obtained. The cross-section contour points are obtained by intercepting the point cloud model with several parallel slices, which is important for the trajectory planning of the spray painting robot. Finally, the uniformity of coating thickness is optimized in terms of the moving speed of the spraying gun and the slice thickness. The simulation and numerical experiment results show that the uniformity of coating thickness and spraying efficiency are improved using the proposed point cloud modeling and slicing algorithm.

The grading size, which can be defined as the side length of the smallest square hole through which an aggregate with irregular shape can directly pass, is an important morphology parameter and can be used to calculate the gradation of mixture material. The grading bounding box, which can be defined as the circumscribed cuboid with central axis length being the grading size, is an important visual tool for observing the size and direction of the aggregate. Virtual test to calculate the grading size of a virtual aggregate is environmentally friendly and efficient, but the result provided by current research is imprecise and the grading bounding box is also rarely mentioned. In this paper, the multilevel complete projection algorithm is proposed to precisely calculate the grading size of a virtual aggregate. The whole process of the algorithm can be expressed by formula after the operation of sphere discretization by converting the virtual aggregate shell into the discrete aggregate. Then, the discrete aggregate is projected onto a complete series of the plane to form several 2D figures, and then, each 2D figure is projected onto a complete series of the orthogonal axis to form orthogonal segments. The grading size can finally be obtained by comparing the length of the above orthogonal segments based on the key central axis length principle. The influencing factors of computational accuracy and efficiency are considered in the algorithm. Finally, the grading bounding box can be built by using the Rodrigues transformation according to the information obtained from the above algorithm.

DC (Difference of Convex functions) programming and DCA (DC Algorithm) play a key role in nonconvex programming framework. These tools have a rich and successful history of thirty five years of development, and the research in recent years is being increasingly explored to new trends in the development of DCA: design novel DCA variants to improve standard DCA, to deal with the scalability and with broader classes than DC programs. Following these trends, we address in this paper the two wide classes of nonconvex problems, called partial DC programs and generalized partial DC programs, and investigate an alternating approach based on DCA for them. A partial DC program in two variables $$(x,y)\in \mathbb {R}^{n}\times {\mathbb {R}}^{m}$$ takes the form of a standard DC program in each variable while fixing other variable. A so-named alternating DCA and its inexact/generalized versions are developed. The convergence properties of these algorithms are established: both exact and inexact alternating DCA converge to a weak critical point of the considered problem, in particular, when the Kurdyka–Łojasiewicz inequality property is satisfied, the algorithms furnish a Frechet/Clarke critical point. The proposed algorithms are implemented on the problem of finding an intersection point of two nonconvex sets. Numerical experiments are performed on an important application that is robust principal component analysis. Numerical results show the efficiency and the superiority of the alternating DCA comparing with the standard DCA as well as a well known alternating projection algorithm.

For solving pseudo-monotone variational inequality problems in Hilbert spaces, we introduce a new algorithm with self-adaptive technique. The algorithm is based on the projection method and inertia...

This paper considers the identification problem of finite impulse response (FIR) systems with binary-valued observations under the assumption of fixed threshold and bounded persistently excitations. A recursive projection algorithm is constructed to estimate the unknown parameter. For first-order FIR systems, the convergence properties of the algorithm are analyzed theoretically. With mild conditions on the weight coefficients in the parameter update, the algorithm is proved to be convergent in mean square and the convergence rate can be the reciprocal of the number of observations, which has the same order as the optimal estimation when the system output is exactly known. Furthermore, it is also shown that the Cramer–Rao (CR) lower bound is achieved asymptotically with proper weight coefficients, which indicates that the algorithm is optimal in the sense of asymptotic efficiency. Some numerical examples are simulated to demonstrate the effectiveness of the proposed algorithm in both first-order and high-order FIR systems.

In this work, a lifted event-triggered iterative learning control (lifted ETILC) is proposed aiming for addressing all the key issues of heterogeneous dynamics, switching topologies, limited resources, and model-dependence in the consensus of nonlinear multi-agent systems (MASs). First, we establish a linear data model for describing the I/O relationships of the heterogeneous nonlinear agents as a linear parametric form to make the non-affine structural MAS affine with respect to the control input. Both the heterogeneous dynamics and uncertainties of the agents are included in the parameters of the linear data model, which are then estimated through an iterative projection algorithm. On this basis, a lifted event-triggered learning consensus is proposed with an event-triggering condition derived through a Lyapunov function. In this work, no threshold condition but the event-triggering condition is used which plays a key role in guaranteeing both the stability and the iterative convergence of the proposed lifted ETILC. The proposed method can reduce the number of control actions significantly in batches while guaranteeing the iterative convergence of tracking error. Both rigorous analysis and simulations are provided and confirm the validity of the lifted ETILC.

The possibility of accelerating a projection algorithm onto dominant singular spaces in the problem of recovering a low-rank matrix from a small number of its entries is explored. The underlying idea is to replace best approximation procedures in the Frobenius norm by fast approximation algorithms. Two methods for computing such approximations are considered: (a) projection onto random subspaces and (b) the cross approximation method. Theorems on the geometric convergence of the algorithms with approximate projections are proved. Numerical experiments are described that demonstrate the efficiency of both variants as compared with the exact projection.

Summary Classical discrete‐time adaptive controllers typically provide asymptotic stabilization and tracking; usually the affect of the noise is at best bounded‐input bounded‐output. Recently we ha...

To solve the problems of small area, slow calculation speed and low precision in the projection transformation algorithm of raster data, the idea of using Kriging interpolation approximate grid algorithm for raster data projection transformation is proposed. Through the experimental results of point-to-point transformation and Kriging interpolation approximate grid algorithm transformation under the same conditions, it can be seen that for different projection types under the same limit conditions, Kriging interpolation approximate grid algorithm can ensure that the raster data projection error is always within the given projection limit. With the same number of points, the Kriging interpolation approximate grid algorithm is faster and more efficient than the point-to-point projection algorithm. Under the same pixel condition, the Kriging interpolation approximate grid algorithm is faster, more accurate and more effective than the point-to-point projection algorithm.

This paper analyses the mechanism of tensor projection transformation in depth and introduces a high-efficiency original algorithm developed in a quantum computing language for forward and backward projection between multidimensional tensors and one-dimensional vectors. Additionally, the author compares this algorithm with similar methods from both the Python scientific computing package and other relative development kits in method calls and source code to demonstrate the innovation of the tensor projection algorithm. On this basis, the classical convolution operation program commonly used in machine learning has been parallelized and improved, the analysis algorithm of the Beidou communication satellite view area has been parallelized and improved, and the actual operating efficiency has been greatly improved. After verification, the tensor projection transformation successfully solves the problem of location index mapping of the entity units among different dimensions, can provide a means for optimizing the traditional model of traversal algorithm, and can have significant reference value in eigenspace transformation against a tensor field.

This paper focuses on the parameter estimation for radial basis function-based state-dependent autoregressive models with moving average noises (RBF-ARMA models). An extended projection algorithm is derived based on the negative gradient search. In order to reduce the sensitivity of the algorithm to noise and reduce the fluctuations of the parameter estimation errors, a modified extended stochastic gradient algorithm is proposed. By introducing a moving data window, a modified moving data window-based extended stochastic gradient algorithm is further developed to improve the parameter estimation accuracy. The simulation results show that the proposed algorithms can effectively estimate the parameters of the RBF-ARMA models.

Interference alignment (IA) in the spatial domain has been recognized as an important technique to handle the interference in dense network. However, traditional IA is flawed especially for large scale antenna systems. With challenges brought by hybrid precoding, IA cannot be perfectly achieved with limited radio frequency (RF) chains. In this article, we adopt the thought of interference subspace alignment (ISA) and provide full digital and hybrid precoding schemes for multi-cell multi-user systems under an interfering broadcast channel model. For full digital precoding, we derive the requirement for transmitting antennas to achieve ISA. A closed-form ISA solution space is further developed, where the interference subspace of each user is no longer constrained. Then, a projection-based ISA algorithm is proposed for full digital precoding. The projection from the selfish design to the ISA solution space strengthens the desired signal while achieving ISA. For hybrid precoding, we formulate a vector approximation problem to minimize interference misalignment. A novel generalized gradient projection algorithm is proposed to design each RF chain. To approximately achieve ISA, two algorithms are proposed with different approximation principles. For low SNR, a specific vector in the ISA solution space is approximated to combat additive noise, while for high SNR, the whole ISA solution space is approximated to suppress interference. The proposed schemes are further extended to imperfect CSI cases for more practical scenarios. Simulation results highlight that the proposed full digital and hybrid precoding schemes can effectively handle the inter-cell and intra-cell interference and outperform the existing schemes.

This paper attempts to focus on the split common fixed point problem for demicontractive mappings. We give an accelerated hybrid projection algorithm which combines the hybrid projection method and the inertial technique. The strong convergence theorems of this algorithm are obtained under mild conditions by a self-adaptive step-size sequence, which does not need prior knowledge of operator norms. Some numerical experiments in infinite Hilbert space are provided to illustrate the reliability and robustness of the algorithm and also to compare it with existin

In this paper, we develop an iterative algorithm whose architecture comprises a modified version of the forward–backward splitting algorithm and the hybrid shrinking projection algorithm. We provide theoretical results concerning weak and strong convergence of the proposed algorithm towards a common solution of the fixed point problem associated to a finite family of demicontractive operators, the split equilibrium problem and the monotone inclusion problem in Hilbert spaces. Moreover, we compute a numerical experiment to show the efficiency of the proposed algorithm. As a consequence, our results improve various existing results in the current literature.

This paper investigates the resource allocation problem for a group of agents communicating over a strongly connected directed graph, where the total objective function of the problem is composted of the sum of the local objective functions incurred by the agents. With local convex sets, we first design a continuous-time projection algorithm over a strongly connected and weight-balanced directed graph. Our convergence analysis indicates that when the local objective functions are strongly convex, the output state of the projection algorithm could asymptotically converge to the optimal solution of the resource allocation problem. In particular, when the projection operation is not involved, we show the exponential convergence at the equilibrium point of the algorithm. Second, we propose an adaptive continuous-time gradient algorithm over a strongly connected and weight-unbalanced directed graph for the reduced case without local convex sets. In this case, we prove that the adaptive algorithm converges exponentially to the optimal solution of the considered problem, where the local objective functions and their gradients satisfy strong convexity and Lipachitz conditions, respectively. Numerical simulations illustrate the performance of our algorithms.

Motivated by the projection technique, in this paper, we introduce a new method for approximating the solution of nonlinear equations with convex constraints. Under the assumption that the associated mapping is Lipchitz continuous and satisfies a weaker assumption of monotonicity, we establish the global convergence of the sequence generated by the proposed algorithm. Applications and numerical example are presented to illustrate the performance of the proposed method.

We consider the convex feasibility problem, which is to determine a point in the intersection of a finite number of closed convex sets. It was shown in the past literature a so-called generalized acceleration method converges to a feasible point in the intersection of all the sets, assuming the intersection set has a nonempty interior. In this letter, we establish the same convergence result without any assumption on the interior of the feasible set. In particular, we devise a randomized accelerated projection algorithm and prove its linear convergence rate when all the convex sets are half-spaces in a finite-dimensional Euclidean space. Numerical experiments comparing the generalized acceleration method with the classic cyclic projection methods are presented, which justify the fast convergence rate and the out-performance of the proposed algorithm.

In this paper, we introduce a shrinking projection method of an inertial type with self-adaptive step size for finding a common element of the set of solutions of a split generalized equilibrium problem and the set of common fixed points of a countable family of nonexpansive multivalued mappings in real Hilbert spaces. The self-adaptive step size incorporated helps to overcome the difficulty of having to compute the operator norm, while the inertial term accelerates the rate of convergence of the proposed algorithm. Under standard and mild conditions, we prove a strong convergence theorem for the problems under consideration and obtain some consequent results. Finally, we apply our result to solve split mixed variational inequality and split minimization problems, and we present numerical examples to illustrate the efficiency of our algorithm in comparison with other existing algorithms. Our results complement and generalize several other results in this direction in the current literature.

The Euclidean projection onto check polytope is the most complicated and time-consuming operation in the alternating direction method of multipliers (ADMM) decoding algorithm for low-density parity-check (LDPC) codes. Existing approximate even-vertex projection algorithm (EVA) can simplify the projection operation, but yields poor decoding performance. By alternately adopting EVA and other accurate projection algorithms, this letter proposes an innovative and simple hybrid projection algorithm (HPA) which can increase the percentage of unuseful projections. Simulation results show that the proposed algorithm can substantially reduce the projection time while achieving better frame error rate (FER) performance when compared with the standard ADMM decoding and the ADMM penalized decoding in the case of avoiding the tedious work of penalty parameter optimization. More importantly, compared with cut search algorithm (CSA), the proposed algorithm can significantly save the average projection time by nearly 80%, and the average decoding time by about 85%.

In this work, we propose a new relaxed projection algorithm for the split feasibility problem with a new linesearch. The proposed method does not require the computation on the matrix inverse and the largest eigenvalue of the matrix. We then prove some weak convergence theorems under suitable conditions in the framework of Hilbert spaces. Finally, we give some numerical examples in signal processing to validate the theoretical analysis results. The obtained results improve the corresponding results in the literature.

In this paper, direction-of-arrival (DOA) estimation in the presence of non-uniform noise is investigated. To achieve high estimation accuracy, the DOA estimation problem is solved with the use of a matrix completion approach. The matrix completion via alternating projection algorithm (APA) is firstly utilized to find the noise-free covariance matrix of the signal, which is then used to find the DOA by utilizing the conventional subspace-based method. Numerical simulations are performed to verify the accuracy and effectiveness of the proposed approach.