Search

In this work, we applied the Supervised Descent Method (SDM) to 3D model-based inversion with limited microwave data. The target shapes are described by parameters based on prior information. The values of these parameters are reconstructed iteratively using SDM in which the descent directions are learned from data set constructed based on prior information. The model-based inversion has less non-uniqueness compared with typical pixel-based inversion. Furthermore, sufficient prior information allows SDM to predict the parameter values with a good accuracy, even with data of limited view. This algorithm is validated using synthetic data. The results show that we can correctly recover target shape parameters with only mono-static reflection data.

For the case of public transport, we consider the problem of demand estimation. Given an origin-destination matrix representing the public transport demand, the distribution of flow among different lines can be obtained assuming that it corresponds to a certain equilibrium characterized by an optimization problem. In particular we will focus on the assignment model proposed by Cepeda et al. (2006). However the knowledge of origin-destination matrix is expensive and sometimes unaffordable in practice. Traditionally, it is estimated using statistical or econometrical considerations. In this work, we explore the estimation through the numerical solution of a bilevel optimization problem. One disadvantage of this formulation is the difficulty of obtaining descent directions, hence, for the resolution of the optimization problem we use a derivative-free method. This method was applied for small networks getting good results.

This paper deals with estimating model parameters in graphical models. We reformulate it as an information geometric optimization problem and introduce a natural gradient descent strategy that incorporates additional meta parameters. We show that our approach is a strong alternative to the celebrated EM approach for learning in graphical models. Actually, our natural gradient based strategy leads to learning optimal parameters for the final objective function without artificially trying to fit a distribution that may not correspond to the real one. We support our theoretical findings with the question of trend detection in financial markets and show that the learned model performs better than traditional practitioner methods and is less prone to overfitting., 18 pages, 9 figures

It is well-known that for general convex optimization problems, block-coordinate descent can get stuck in poor local optima. Despite that, versions of this method known as convergent message passing are very successful to approximately solve the dual LP relaxation of the MAP inference problem in graphical models. In attempt to identify the reason why these methods often achieve good local minima, we argue that if in block-coordinate descent the set of minimizers over a variable block has multiple elements, one should choose an element from the relative interior of this set. We show that this rule is not worse than any other rule for choosing block-minimizers. Based on this observation, we develop a theoretical framework for block-coordinate descent applied to general convex problems. We illustrate this theory on convergent message-passing methods.

The robust result of analytical fuzzy reliability analysis (FRA) represents the main effort at evaluating the fuzzy reliability index. In this study, a bioloop-based hybrid method is propos...

In this paper, we study a hybrid forward&ndash, backward algorithm for sparse reconstruction. Our algorithm involves descent, splitting and inertial ideas. Under suitable conditions on the algorithm parameters, we establish a strong convergence solution theorem in the framework of Hilbert spaces. Numerical experiments are also provided to illustrate the applications in the field of signal processing.

Controlling large particle systems in collective dynamics by a few agents is a subject of high practical importance, e.g., in evacuation dynamics. In this paper we study an instantaneous control approach to steer an interacting particle system into a certain spatial region by repulsive forces from a few external agents, which might be interpreted as shepherd dogs leading sheep to their home. We introduce an appropriate mathematical model and the corresponding optimization problem. In particular, we are interested in the interaction of numerous particles, which can be approximated by a mean-field equation. Due to the high-dimensional phase space this will require a tailored optimization strategy. The arising control problems are solved using adjoint information to compute the descent directions. Numerical results on the microscopic and the macroscopic level indicate the convergence of optimal controls and optimal states in the mean-field limit,i.e., for an increasing number of particles., Comment: arXiv admin note: substantial text overlap with arXiv:1610.01325

The physical support of the Internet infrastructure is fiber-optics network (FON). Since the global Internet traffic doubles each year, FONs are suffering the capacity crunch problem, and several proposals offer content-oriented solutions, combined with a smart spectral utilization.It is well known that the physical implementation of FONs is robust under single failures on its links, or 2-connected. Unfortunately, simultaneous failures occur, and the service is disrupted for some hours per year in average.In this paper we propose a smart network augmentation which solves the previous problems simultaneously. The resulting network is a locally most-reliable 3-connected augmentation. Our methodology to build 3-connected networks is supported by the theory of uniformly most-reliable networks, elementary properties of cubic networks and a careful selection of local searches in a Variable Neighborhood Descent (VND) metaheuristic.

In this article, a deterministic annealing neural network algorithm is proposed to solve the minimum concave cost transportation problem. Specifically, the algorithm is derived from two neural network models and Lagrange–barrier functions. The Lagrange function is used to handle linear equality constraints, and the barrier function is used to force the solution to move to the global or near-global optimal solution. In both neural network models, two descent directions are constructed, and an iterative procedure for the optimization of the neural network is proposed. As a result, two corresponding Lyapunov functions are naturally obtained from these two descent directions. Furthermore, the proposed neural network models are proved to be completely stable and converge to the stable equilibrium state, therefore, the proposed algorithm converges. At last, the computer simulations on several test problems are made, and the results indicate that the proposed algorithm always generates global or near-global optimal solutions.

The idea that the brain functions so as to minimize certain costs pervades theoretical neuroscience. Because a cost function by itself does not predict how the brain finds its minima, additional assumptions about the optimization method need to be made to predict the dynamics of physiological quantities. In this context, steepest descent (also called gradient descent) is often suggested as an algorithmic principle of optimization potentially implemented by the brain. In practice, researchers often consider the vector of partial derivatives as the gradient. However, the definition of the gradient and the notion of a steepest direction depend on the choice of a metric. Because the choice of the metric involves a large number of degrees of freedom, the predictive power of models that are based on gradient descent must be called into question, unless there are strong constraints on the choice of the metric. Here, we provide a didactic review of the mathematics of gradient descent, illustrate common pitfalls of using gradient descent as a principle of brain function with examples from the literature, and propose ways forward to constrain the metric., PLoS Computational Biology, 16 (4), ISSN:1553-734X, ISSN:1553-7358

[EN] Solving optimization problems using heuristic algorithms requires the selection of its parameters. Traditionally, these parameters are selected by a trial and error process that cannot guarantee the quality of the results obtained because not all the potential combinations of parameters are checked. To fill this gap, this paper proposes the application of Taguchi's orthogonal arrays to calibrate the parameters of a heuristic optimization algorithm (the descent local search algorithm). This process is based on the study of the combinations of discrete values of the heuristic tool parameters and it enables optimization of the heuristic tool performance with a reduced computational effort. To check its efficiency, this methodology is applied to a technical challenge never studied before: the optimization of the tensioning process of cable-stayed bridges. The statistical improvement of the heuristic tool performance is studied by the optimization of the tensioning process of a real cable-stayed bridge. Results show that the proposed calibration technique provided robust values of the objective function (with lower minimum and mean values, and lower standard deviation) with reduced computational cost., The authors are indebted to the Spanish Ministry of Economy and Competitiveness for the funding provided through the research projects BIA2013-47290-R and BIA2017-86811-C2-1-R founded with FEDER funds and directed by Professor Jose Turmo and through the research project BIA2017-86811-C2-2-R directed by Jose Antonio Lozano-Galant.

We propose a two-layer, semi-decentralized algorithm to compute a local solution to the Stackelberg equilibrium problem in aggregative games with coupling constraints. Specifically, we focus on a single-leader, multiple follower problem, and after equivalently recasting the Stackelberg game as a mathematical program with complementarity constraints (MPCC), we iteratively convexify a regularized version of the MPCC as inner problem, whose solution generates a sequence of feasible descent directions for the original MPCC. Thus, by pursuing a descent direction at every outer iteration, we establish convergence to a local Stackelberg equilibrium. Finally, the proposed algorithm is tested on a numerical case study, a hierarchical instance of the charging coordination problem of Plug-in Electric Vehicles (PEVs).

We suggest a modified descent splitting method for optimization problems having a special decomposable structure. The proposed modification maintains the basic convergence properties but enables one to reduce computational efforts per iteration and to provide computations in a distributed manner. On the one hand, it consists in component-wise choice of descent directions together with a special threshold control. On the other hand, it involves a simple adaptive step-size choice, which takes into account the problem behavior along the iteration sequence. Preliminary computational tests confirm the efficiency of the proposed modification.

Block-coordinate descent (BCD) is a popular method in large-scale optimization. Unfortunately, its fixed points are not global optima even for convex problems. A succinct characterization of convex problems optimally solvable by BCD is unknown. Focusing on linear programs, we show that BCD fixed points are identical to fixed points of another method, which uses constraint propagation to detect infeasibility of a system of linear inequalities in a primal-dual loop (a special case of this method is the Virtual Arc Consistency algorithm by Cooper et al.). This implies that BCD fixed points are global optima iff a certain propagation rule decides feasibility of a certain class of systems of linear inequalities.

This paper uses a graphic engine to simulate a large amount of training data with free annotations. Between synthetic and real data, there is a two-level domain gap, i.e., content level and appearance level. While the latter has been widely studied, we focus on reducing the content gap in attributes like illumination and viewpoint. To reduce the problem complexity, we choose a smaller and more controllable application, vehicle re-identification (re-ID). We introduce a large-scale synthetic dataset VehicleX. Created in Unity, it contains 1,362 vehicles of various 3D models with fully editable attributes. We propose an attribute descent approach to let VehicleX approximate the attributes in real-world datasets. Specifically, we manipulate each attribute in VehicleX, aiming to minimize the discrepancy between VehicleX and real data in terms of the Frechet Inception Distance (FID). This attribute descent algorithm allows content domain adaptation (DA) orthogonal to existing appearance DA methods. We mix the optimized VehicleX data with real-world vehicle re-ID datasets, and observe consistent improvement. With the augmented datasets, we report competitive accuracy. We make the dataset, engine and our codes available at https://github.com/yorkeyao/VehicleX.

Over-parameterized deep neural networks (DNNs) with sufficient capacity to memorize random noise can achieve excellent generalization performance, challenging the bias-variance trade-off in classical learning theory. Recent studies claimed that DNNs first learn simple patterns and then memorize noise; some other works showed a phenomenon that DNNs have a spectral bias to learn target functions from low to high frequencies during training. However, we show that the monotonicity of the learning bias does not always hold: under the experimental setup of deep double descent, the high-frequency components of DNNs diminish in the late stage of training, leading to the second descent of the test error. Besides, we find that the spectrum of DNNs can be applied to indicating the second descent of the test error, even though it is calculated from the training set only., Comment: IJCAI-21. Int'l Joint. Conf. on Artificial Intelligence (IJCAI), Montreal, Canada, August 2021

The renewed interest in Steepest Descent (SD) methods following the work of Barzilai and Borwein [IMA Journal of Numerical Analysis, 8 (1988)] has driven us to consider a globalization strategy based on SD, which is applicable to any line-search method. In particular, we combine Newton-type directions with scaled SD steps to have suitable descent directions. Scaling the SD directions with a suitable step length makes a significant difference with respect to similar globalization approaches, in terms of both theoretical features and computational behavior. We apply our strategy to Newton's method and the BFGS method, with computational results that appear interesting compared with the results of well-established globalization strategies devised ad hoc for those methods., Comment: 22 pages, 11 Figures

In this paper, a Cauchy point direction trust region algorithm is presented to solve nonlinear equations. The search direction is an optimal convex combination of the trust region direction and the Cauchy point direction with the sufficiently descent property and the automatic trust region property. The global convergence of the proposed algorithm is proven under some conditions. The preliminary numerical results demonstrate that the proposed algorithm is promising and has better convergence behaviors than the other two existing algorithms for solving large-scale nonlinear equations.

This paper considers a refinement problem for the flight altitude, speed, and flight-path angle of an aircraft during aerodynamic deceleration in the atmosphere of Mars using inaccurate discrete g-load measurements. For solving this problem, several suboptimal discrete nonlinear filters of higher accuracy than the extended Kalman filter based on the Taylor linearization procedure with static (Gaussian) linearization of the nonlinearities are applied and compared with each other. The equations of these filters are derived, the Gaussian moments of their structural functions are calculated, and the resulting accuracy of these filters is analyzed in statistical terms.

This paper develops a distributed discrete-time algorithm to seek Nash equilibrium for games under Markovian switching topologies. In the game problem considered in this paper, all players are assumed to use gradient-like descent method to update their own actions based on the estimation of all the other players’ actions with the intention to minimize their cost functions. All players exchange their estimation information with their neighbors at each discrete time instant through some undirected graphs that are Markovian switching. Suppose that the transition probability matrix is specified and the union of all switching topologies is connected, it is shown that the players’ actions can converge to the unique Nash equilibrium in the mean square sense for any initial condition. The convergence result is established by utilizing Lyapunov stability theory for discrete-time stochastic systems.

This paper present algorithms for solving a single machine scheduling problem to minimize the sum of total completion times, total tardiness,maxim-um tardiness,and maximum earliness.The single machine total tardiness problem is already NP-hard, so the consider problem is strongly NP-hard, and several algorithms are used to solve it. Branch and bound algorithmwith dominance ruleand local search algorit- hms are proposed for the problem. For the Branch and bound algorithm results- show that using dominance rule improve the performance of the algorithm in both computation times and optimal values,but it need longer times.Thus we tackle the problemof large sizes with local search algorit- hms descent method, simulated annealing and tabusearch. The perfomance of these algorithms is evaluated on a large set of test problems and the results are compared.The computational results show that simulated annealing algorithm and Tabu search algorithm are better than Descent method with preference to simulated annealing algorithm,and show that the three algorithms find optimal or near optimal solutions inreasonable times.

Focusing on the trajectory curvature, this paper presents an innovative and analytical guidance law for the construction of geometrically convex trajectories. Moving along such trajectories, the lander can increase the probability of a safe landing in hazardous terrains. Initially, the curvature theorems of the powered descent trajectories are developed. In these theorems, the inner relationship between trajectory curvature and lander states is revealed, and the state constraints for a geometrically convex trajectory are derived. Next, the trajectory curvature guidance is developed in an analytical formulation by satisfying the state constraints for a convex trajectory, and the selection of the key guidance parameters is investigated. Finally, the performance of the trajectory curvature guidance is analyzed in detail, illustrating its superior hazard avoidance and the camera’s field of view.

An innovative computational guidance framework is proposed for planetary powered descent using collaborative optimization approach. First, the dynamical model and constraints for planetary powered descent are presented. Then, using collaborative optimization strategy, the computational guidance framework for powered descent is formulated as a multi-discipline optimization problem including trajectory optimization, optimal guidance, and system-level optimization. Finally, the computational guidance approach employs three algorithms for respectively solving the three optimization modules to implement numerical simulations. The optimality and robustness of the computational guidance approach are verified with all constraints satisfied even in the presence of initial state uncertainty.

Some methods for finding the maximum feasible subsystems of systems of linear inequalities are considered. The problem of finding the most accurate algorithm in a parametric family of linear classification algorithms is one of the most important problems in machine learning. In order to solve this discrete optimization problem, an exact (combinatorial) algorithm, its approximations (relaxation and greedy combinatorial descent algorithms), and the approximation algorithm are given. The latter consists in replacing the original discrete optimization problem with a nonlinear programming problem by changing from linear inequalities to their sigmoid functions. The initial results of their comparison are presented.

Although different satisfiability decision procedures can be combined by algorithms such as those of Nelson–Oppen or Shostak, current tools typically can only support a finite number of theories to use in such combinations. To make SMT solving more widely applicable one needs theory-generic satisfiability algorithms allowing a potentially infinite number of decidable theories to be user-definable, instead of needing to be built in by tool implementers. This work studies how folding variant narrowing, a generic unification algorithm that offers good extensibility in unification theory, can be extended to a generic variant-based satisfiability algorithm for the initial algebras of user-specified input theories when such theories satisfy Comon and Delaune's finite variant property (FVP) and some extra conditions. Several, increasingly larger infinite classes of theories whose initial algebras enjoy decidable variant-based satisfiability are identified and illustrated with examples. A method based on descent maps to bring other theories into these classes and to improve the generic algorithm's efficiency is also proposed.

This paper gives a modified Hestenes and Stiefel (HS) conjugate gradient algorithm under the Yuan-Wei-Lu inexact line search technique for large-scale unconstrained optimization problems, where the proposed algorithm has the following properties: (1) the new search direction possesses not only a sufficient descent property but also a trust region feature; (2) the presented algorithm has global convergence for nonconvex functions; (3) the numerical experiment showed that the new algorithm is more effective than similar algorithms.

We revisit the static coverage control problem for placement of vehicles with simple motion on the real line, under the assumption that the cost is a polynomial function of the locations of the vehicles. The main contribution of this paper is to demonstrate the use of tools from numerical algebraic geometry, in particular, a numerical polynomial homotopy continuation method that guarantees to find all solutions of polynomial equations, in order to characterize the \emph{global minima} for the coverage control problem. The results are then compared against a classic distributed approach involving the use of Lloyd descent, which is known to converge only to a local minimum under certain technical conditions., 6 pages, 2 figures

Optic disc (OD) segmentation is an important step in analyzing the color fundus image. Most existing approaches are based on the shape prior and visual appearance of the OD boundary. However, the current ways of integrating the shape and appearance are simple. We argue that the performance of OD segmentation can be improved by better shape-appearance modeling. In this paper, we propose to learn a sequence of supervised descent directions between the coordinates of OD boundary and their surrounding visual appearances for OD segmentation. In addition, we introduce the histograms of gradient orientations to represent the OD appearance. Experimental results on six datasets clearly show that the proposed method improves the OD segmentation and outperforms the state-of-the-art.

One important problem in radiation therapy for cancer treatment is the selection of the set of beam angles radiation will be delivered from. A primary goal in this problem is to find a beam angle configuration (BAC) that leads to a clinically acceptable treatment plan. Further, this process must be done within clinically acceptable times. Since the problem of selecting beam angles in radiation therapy is known to be extremely hard to solve as well as time-consuming, both exact algorithms and population-based heuristics might not be suitable to solve this problem. In this paper, we compare two matheuristic methods based on local search algorithms, to approximately solve the beam angle optimisation problem (BAO). Although the steepest descent algorithm is able to find locally optimal BACs for the BAO problem, it takes too long before convergence, which is not acceptable in clinical practice. Thus, we propose to use a next descent algorithm that converges quickly to good quality solutions although no (local) optimality guarantee is given. We apply our two matheuristic methods on a prostate case which considers two organs at risk, namely, the rectum and the bladder. Results show that the matheuristic algorithm based on the next descent local search is able to quickly find solutions as good as the ones found by the steepest descent algorithm.

In this paper, we propose a distributed algorithm, called Directed-Distributed Subgradient Descent (D-DSD), to solve multi-agent optimization problems over directed graphs. Existing algorithms mostly deal with similar problems under the assumption of undirected networks, i.e., requiring the weight matrices to be doubly-stochastic. The row-stochasticity of the weight matrix guarantees that all agents reach consensus, while the column-stochasticity ensures that each agent’s local (sub)gradient contributes equally to the global objective. In a directed graph, however, it may not be possible to construct a doubly-stochastic weight matrix in a distributed manner. We overcome this difficulty by augmenting an additional variable for each agent to record the change in the state evolution. In each iteration, the algorithm simultaneously constructs a row-stochastic matrix and a column-stochastic matrix instead of only a doubly-stochastic matrix. The convergence of the new weight matrix, depending on the row-stochastic and column-stochastic matrices, ensures agents to reach both consensus and optimality. The analysis shows that the proposed algorithm converges at a rate of O ( ln k k ) , where k is the number of iterations.

The soft-clustered vehicle-routing problem (SoftCluVRP) is a variant of the classical capacitated vehicle-routing problem. Customers are partitioned into clusters and all customers of the same cluster must be served by the same vehicle. In this paper, we present a large multiple neighborhood search for the SoftCluVRP. We design and analyze multiple cluster destroy and repair operators as well as two post-optimization components, which are both based on variable neighborhood descent. The first allows inter-route exchanges of complete clusters, while the second searches for intra-route improvements by combining classical neighborhoods (2-opt, Or-opt, double-bridge) and the Balas-Simonetti neighborhood. Computational experiments show that our algorithm clearly outperforms the only existing heuristic approach from the literature. By solving benchmark instances, we provide 130 new best solutions for 220 medium-sized instances with up to 483 customers and prove 12 of them to be optimal. Furthermore, we describe a straightforward adaption of our algorithm to the clustered vehicle-routing problem, a variant of the SoftCluVRP.

A multi-period, multi-echelon, multi-product, and multi-modal sustainable supply chain network design problem is considered. The problem is formulated as a multi-objective Mixed-Integer Linear Programming (MILP) model that explicitly considers the environmental footprint and social responsibilities. We introduce the Multi-Neighborhood Descent Traversal Algorithm (MNDTA), which can solve this problem efficiently. The MNDTA begins with a structured initial solution of the model and improves the incumbent solution by sequentially traversing several specifically designed neighborhoods over generations. A lower-bound-based evaluation method is introduced to reduce the computational complexity involved in solving the integer programming problem. Experimental results demonstrate that the proposed MNDTA can provide high-quality solutions that are close to the optimal solutions with a negligibly small (relative) gap and can solve large instances much more quickly than CPLEX can. In addition, the MNDTA outperforms existing solution algorithms. A numerical comparison of the results of the proposed model with those of a model that only considers financial aspects demonstrates that explicitly using our model when designing a supply chain network can substantially reduce the environmental impact and increase social responsibility at a negligible cost increase.

The goal of this paper is to examine the possible neurobiological basis of a defining property of the human language faculty: recursion. I suggest that recursion should be understood in light of Darwinian's descent with modification. Descent: that is, based on ingredients of neural circuitry found in ‘non-linguistic’ species; and modification: a reconfiguration that is specific to anatomically modern humans. I argue that the expansion of the parietal region associated with the globularization of the neurocranium in our species contributed to the transformation of the connection between Broca's and Wernicke's region via Geschwind's territory, and enabled the pairing of evolutionary ancient networks that together became capable of constructing and processing not just sequences, but sequences of sequences.

In this paper, we present a new nonmonotone memory gradient algorithm for unconstrained optimization problems. An attractive property of the proposed method is that the search direction always provides sufficient descent step at each iteration. This property is independent of the line search used. Under mild assumptions, the global and local convergence results of the proposed algorithm are established respectively. Numerical results are also reported to show that the proposed method is suitable to solve large-scale optimization problems and is more stable than other similar methods in practical computation.

In this study, we introduce a new global optimization method, named Esthetic Delving Method, based on the auxiliary function approach. First, we design the method theoretically and then present its implementable version. Finally, we apply the algorithm to the test problems in order to demonstrate its efficiency.

The authors considered the solution of boundary problems, arising from objects modeling with distributed parameters, of radial basis functions networks. The gradient algorithms analysis for learning radial basis functions networks when solving boundary value problems is carried out. The widely used the first order method-the gradient method descent does not provide high learning rate and the solution accuracy. The fastest of the second order method - the method of trust regions is very complicated. Developed implementations of the first order method-the accelerated Nesterov gradient and the second order method-Levenberg Marquardt for learning radial basic functions networks in solving boundary value problems. A comparison is made of the Levenberg Marquardt methods and trust regions for learning radial basis functions networks. The results are presented of solving model problem using the developed methods. The Levenberg-Marquardt method, with a simpler implementation, showed the results compared with the fastest method of the second order - the method of trust regions.

In this work, we study the application of the supervised descent method using neural networks (SDMNN) for 2D electrical impedance tomography. SDMNN contains the offline training and the online prediction stages. In the offline stage, neural networks are iteratively applied to learn a set of descent directions for minimizing the objective function; in the online stage, the trained neural networks can be directly used for the image reconstruction. This scheme combines the advantages of fast convergence speed of neural networks and good generalization ability of the supervised descent method (SDM). Numerical results verify the efficiency and accuracy of this method.

We propose an unsupervised method for saliency detection with multiple functions by a universal descent model. The basic descent model is concise, which is a minimization equation conducted by a relationship matrix and background prior. The relationship matrix is calculated by the contrast of features which contains much information between superpixels. So saliency maps with high performance can be obtained even if only one feature is included. Besides, various terms can be appended to the basic descent model to achieve multiple functions. For example, considering an neighbor matrix into the basic model can further smooth saliency maps. The refinement term can also refine existing results by introducing prior saliency maps, demonstrating the universal applications of our model. Extensive experiments on different datasets indicate that the basic model outperforms state-of-the-art methods. The universal descent models with smoothness and refinement terms are able to promote the performance of state-of-the-art methods by a large margin.

This paper describes an optimization technique of neural networks radial basis function multi-model identification of nonlinear system. Indeed, this paper treats the multi-model approach based on parametric identification. The used architecture of the neural multi-model is radial basis function. We have used the descent gradient and the genetic algorithm technique and we have compared the found results. The effectiveness of the proposed approach is shown through a numerical simulation of a nonlinear system and we have confirmed that the genetic algorithm give a very good results.

We propose a policy search method for synthesizing optimal feedback control laws for reference tracking directly from data. During the learning phase, the control law is optimized by using stochastic gradient descent iterations and (optionally) applied to the plant while collecting data. Differently from model-based methods, in which a full model of the open-loop plant is first identified from data, here a simple linear model is recursively identified with forgetting factor for the only reason of computing approximately the gradients required for the descent. We report examples showing that the method recovers the optimal feedback law in case the underlying plant is linear, and outperforms the best control law that is achieved by first identifying an open-loop linear model in case the underlying plant is nonlinear.

In this paper, we consider the large-scale case of the robust beamforming problem with interference temperature constraints. Previous semidefinite relaxation (SDR) method becomes impracticable because of its expensive computational cost. Even successive convex approximation (SCA) method, the state-of-the-art method, cannot tackle this problem efficiently. Thus, we are motivated to design two efficient first-order methods, multi-block alternating direction method of multipliers (ADMM) and linear programming-assisted subgradient descent (LPA-SD), to solve it. Numerical results demonstrate the potential of our proposed methods in terms of both computational efficiency and solution quality.

This paper investigates different vector step-size adaptation approaches for non-stationary online, continual prediction problems. Vanilla stochastic gradient descent can be considerably improved by scaling the update with a vector of appropriately chosen step-sizes. Many methods, including AdaGrad, RMSProp, and AMSGrad, keep statistics about the learning process to approximate a second order update---a vector approximation of the inverse Hessian. Another family of approaches use meta-gradient descent to adapt the step-size parameters to minimize prediction error. These meta-descent strategies are promising for non-stationary problems, but have not been as extensively explored as quasi-second order methods. We first derive a general, incremental meta-descent algorithm, called AdaGain, designed to be applicable to a much broader range of algorithms, including those with semi-gradient updates or even those with accelerations, such as RMSProp. We provide an empirical comparison of methods from both families. We conclude that methods from both families can perform well, but in non-stationary prediction problems the meta-descent methods exhibit advantages. Our method is particularly robust across several prediction problems, and is competitive with the state-of-the-art method on a large-scale, time-series prediction problem on real data from a mobile robot., Comment: AAAI Conference on Artificial Intelligence 2019. v2: Correction to Baird's counterexample. A bug in the code lead to results being reported for AMSGrad in this experiment, when they were actually results for Adam

Many problems in smart solution development make use of discrete optimization techniques. It is expected that smart cities will have a constant need for parcel delivery and vehicle routing which is heavily reliant on discrete optimization. In this paper we present an improvement to the Variable neighborhood descent (VND) algorithm for discrete optimization. Our method makes the search procedure more exhaustive at the expense of time performance. Instead of keeping track of a single solution which is being improved, we allow branching of the solution into at most M promising solutions and keep track of them. Our experiments show that the proposed method produces results superior to VND. We analyze the impact on time complexity and give general usage guidelines for our method.

In this study, we tend to propose a replacement hybrid algorithmic rule which mixes the search directions like Steepest Descent (SD) and Quasi-Newton (QN). First, we tend to develop a replacement search direction for combined conjugate gradient (CG) and QN strategies. Second, we tend to depict a replacement positive CG methodology that possesses the adequate descent property with sturdy Wolfe line search. We tend to conjointly prove a replacement theorem to make sure global convergence property is underneath some given conditions. Our numerical results show that the new algorithmic rule is powerful as compared to different standard high scale CG strategies.

In this paper, a stochastic trust region method is proposed to solve unconstrained minimization problems with stochastic objectives. Particularly, this method can be used to deal with nonconvex problems. At each iteration, we construct a quadratic model of the objective function. In the model, stochastic gradient is used to take the place of deterministic gradient for both the determination of descent directions and the approximation of the Hessians of the objective function. The behavior and the convergence properties of the proposed method are discussed under some reasonable conditions. Some preliminary numerical results show that our method is potentially efficient.

Supervised Descent Method (SDM) is an efficient and accurate approach for facial landmark locating and face alignment. In the training phase, it requires a large amount of training samples to learn the descent directions and get the corresponding regressors. Then in the test phase, it uses the corresponding regressors to estimate the descent directions and locate the facial landmarks. However, when the facial expression or direction changes too much, generally SDM cannot obtain good performance due to the large variation between the initial shape (the initial shape of SDM is the mean shape of the training samples) and the target shape. Therefore, we propose a coarse-to-fine SDM (CFSDM) method to improve the accuracy of the test results. This method predicts the approximate coordinates of the facial landmarks with a simple CNN (Convolutional Neural Network) network (here we introduce the channel-wise attention mechanism, which can predict the coordinates of the landmarks more accurately with a relatively simple structure) in advance, and then SDM will take the coordinates as its initial shape’s coordinates, which reduces the distance between the initial shape and the target shape, thereby solving the problem that SDM cannot achieve good results when the facial expression or direction changes greatly.

Variable neighborhood searches and evolutionary techniques have shown their effectiveness when dealing with many combinatorial optimisation problems. This study proposes to combine these two techniques for addressing the routing problem using electric and modular vehicles. This is a recent problem that aims to overcome recharging battery constraints while maintaining a certain performance regarding to the fleet cost and the traveled distance. An experimental study on benchmark instances is provided to show the relevance of the proposed algorithm.

This paper introduces a continuous formulation for compound state-triggered constraints, which are generalizations of the recently introduced state-triggered constraints. State-triggered constraints are different from ordinary constraints found in optimal control in that they use a state-dependent trigger condition to enable or disable a constraint condition, and can be expressed as continuous functions that are readily handled by successive convexification. Compound state-triggered constraints go a step further, giving designers the ability to compose trigger and constraint conditions using Boolean and and or operations. Simulations of the 6-degree-of-freedom (DoF) powered descent guidance problem obtained using successive convexification are presented to illustrate the utility of state-triggered and compound state-triggered constraints. The examples employ a velocity-triggered angle of attack constraint to alleviate aerodynamic loads, and a collision avoidance constraint to avoid large geological formations. In particular, the velocity-triggered angle of attack constraint demonstrates the ability of state-triggered constraints to introduce new constraint phases to the solution without resorting to combinatorial techniques., Comment: This paper is a modified version of the one presented at the 2019 AIAA Guidance, Navigation, and Control Conference (SciTech) in San Diego, California (17 pages, 10 figures)