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To solve the control problem of time-varying state-scale nonlinear systems whose initial state is not affected by settling time, fixed-time convergence algorithms are proposed for first-order systems and higher-order systems in this paper. First, a scalar model is used to illustrate how the time-varying feedback parameter can guarantee that the system achieves asymptotic stability while achieving finite-time convergence, and it is proved that the settling time obtained in this paper is only related to the prescribed boundary. This allows us to design the settling time with an appropriate parameter based on the prescribed boundary. To exhibit the effectiveness and extensibility of the proposed algorithm for first-order scalar systems, the results are subsequently extended to general higher-order systems based on the backstepping method. By introducing numerical simulation results, this paper verifies that the proposed algorithm will make the system achieve asymptotic stability and its output can converge to a given boundary, regardless of the system's initial states. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce a forward-backward-forward algorithm with inertial extrapolation to solve the problem of finding a common solution to the variational inequality problem (CSVIP) in a Hadamard manifold. Using a self-adaptive step size, we obtain convergence results under some standard conditions. Numerical examples are given to illustrate the theoretical analysis. Our result is a generalization and extension of previously announced results in this direction in the literature. [ABSTRACT FROM AUTHOR]

This paper attempts to propose two adaptive nonmonotone trust-region algorithms in the multiobjective optimization (MO) case. The first proposed trust-region algorithm uses a modified maximum nonmonotone technique, which takes a convex combination of the maximum value of some preceding successful iterates and the function value in the current iterate. The second one employs the average nonmonotone technique, which takes a weighted average of the successive function values. Under some suitable assumptions, the convergence of the sequences generated by the trust-region algorithms that use the aforementioned nonmonotone techniques to a critical point is shown. Using some well-known test problems, we compare our proposed adaptive nonmonotone MO algorithms with some other MO trust-region algorithms. To conduct a thorough comparison in this regard, some performance criteria are used. These numerical results confirm a significant advantage of applying the proposed adaptive nonmonotone trust-region algorithms in solving MO problems. Finally, the proposed algorithms are implemented to optimize one of the optimization problems of the abrasive water-jet machining process. [ABSTRACT FROM AUTHOR]

The paper concerns a new iterative method for approximating a solution of an equilibrium problem involving a monotone and Lipschitz-type bifunction in a Hilbert space. Our method combines the proximal mapping with a regularization technique. When compared with known extragradient methods, the proposed method is seen to have a simpler and more elegant structure. A strong convergence theorem is established under some appropriate conditions imposed on the control parameters. Several experiments are performed in order to illustrate the numerical effectiveness of our new algorithm in comparison with that of existing methods. [ABSTRACT FROM AUTHOR]

In this paper, we study split common fixed point problems with multiple output sets in Hilbert spaces. For solving this problem, we improve Reich and Tuyen's algorithms [10] and propose two new self-adaptive algorithms which do not need any priori information on the norms of the transfer operators. Then, we establish weak convergence theorems for them. It can be seen from our numerical experiments that the proposed methods depict a very significant improvement in terms of the number of iterations and execution time. [ABSTRACT FROM AUTHOR]

In this paper, we mainly consider a class of nonconvex non smooth optimization problems, whose objective function is the sum of a smooth function with a Lipschitz continuous gradient and a convex non smooth function. We first propose a proximal stochastic recursive momentum algorithm(ProxSTORM) with mini-batch for solving the optimization problems and consider its convergence behaviour. Then, based on the Polyak–Łojasiewicz inequality, we establish the global linear convergence rate of ProxSTORM. Finally, some numerical experiments have been conducted to illustrate the efficiency of our method. [ABSTRACT FROM AUTHOR]

This paper focuses on the constrained minimax location problem with the closest distance. Some properties concerning the existence and uniqueness of the optimal solution are provided. To achieve these results, we apply non-smooth approach that allow us to give the explicit solution structure of the constrained problem. Moreover, we develop an effective algorithm for solving this class of problems and we provide its convergence under some mild assumptions. At the end, some computational test problems are provided to illustrate the effectiveness of the method and certify the theoretical results. [ABSTRACT FROM AUTHOR]

With the rapid development of social platforms and human activities, people are now interested to solve their problems with the help of the social crowd-powered system. So, crowdsourcing has become a promising way of solving problems in a distributed manner within a specific time. Crowd workers pick up a task (simple or complex) and solve it with competing interest or collaboratively and receive an incentive (as monetary or non-monetary). In paid crowdsourcing platforms, crowd workers solve complex tasks and get remunerations through prior bidding or prior announcement of fee decided by the requester (task provider). For decomposable tasks, a single winner may not provide a significant solution to the requester due to the insufficient knowledge. So, we induce collaboration in competitive crowdsourcing markets to better handle decomposable-type tasks. In this paper, we propose an envelope game-based mechanism that ensures if the tasks are decomposable then the workers will be encouraged to collaborate with their subtasks and share their remunerations. This mechanism also increases the chance of receiving more number of cost-effective solutions. Thus both the requester and crowd workers get benefits from the system. The effectiveness of the proposed mechanism is evaluated through empirical analysis on simulated environments. [ABSTRACT FROM AUTHOR]

Security of vector maps is of importance in the community of geographic information sciences. Although some encryption techniques can protect vector maps from piracy, they need to decrypt the entire map in order to extract parts of the data, which obviously brings inconvenience to the users. To solve the problem, an encryption algorithm for vector maps based on Gaussian random and Haar transform is proposed in this paper. First, all vertices are randomized via the Gaussian random method to get the shuffled vector map coordinates. Then, the average coefficient and the differential coefficient generated by the Haar transform are encrypted. Lastly, the encrypted map data is obtained through performing the inverse Haar transformation. Experiments show that (1) the proposed algorithm guarantees authorized users can decrypt any parts (layers) of encrypted vector maps; and (2) the algorithm outperforms other existing encryption methods in security and efficiency. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the problem of finding fixed points of nonexpansive mappings on Hadamard manifolds. To solving this kind of problem, a modified Riemannian Halpern algorithm, which is a natural generalization of a modified Halpern algorithm in Euclidean space is proposed. By giving some mild assumptions and necessary lemmas, the global convergence of the proposed algorithm is established. Finally, when the problem is solved in the framework of Hadamard manifolds, the numerical experiments show the effectiveness of the proposed algorithm, especially in computational time and number of iterations. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the split equilibrium problems and fixed point problems in Hilbert spaces. We provide a unified framework for solving such problem in which the involved equilibrium bifunctions f and g are pseudomonotone and monotone, respectively, and the operators S and T are pseudocontractive. We suggest an iterative algorithm for solving the split problem and demonstrate its weak convergence. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the problem of solving strongly monotone variational inequality problems over the solution set of the split feasibility problem with multiple output sets in real Hilbert spaces. The strong convergence of the proposed algorithm is proved without knowing any information of the Lipschitz and strongly monotone constants of the mapping. In addition, the implementation of the algorithm does not require the computation or estimation of the norms of the given bounded linear operators. Special cases are considered. Finally, a numerical experiment has been carried out to illustrate the proposed algorithm. [ABSTRACT FROM AUTHOR]

In the era of big data, structural variation and heterogeneity of high-dimensional data bring a great challenge to statistical modelling and computation. In this paper, wepropose a high-dimensional continuous threshold model for such data and develop a regularized expectile framework with the non-convex SCAD penalty. Due to theexistence of threshold, we have to tackle a non-linear and non-differentiable optimization problem. Inspired by the linear reparameterization technique and LLA strategy,we propose an efficient algorithm to solve this problem. Theoretical analysis and simulation results show that compared with the classical grid-search method, ouralgorithm has considerable computational advantages. Besides, our proposed method also performs well in variable selection, parameter estimation, thresholdidentification and data heterogeneity detection. These results indicate that our proposed method is effective in analysing high-dimensional heterogeneous data. [ABSTRACT FROM AUTHOR]

This paper presents a new numerical method to solve the non-linear constitutive equations of viscoelastic string with variable fractional order model. Firstly, the non-linear constitutive equation of the string is established based on the variable fractional viscoelastic model. Secondly, non-linear constitutive equation of the string is transformed into a matrix equation by using Bernstein polynomials, which can greatly simplify the solving process. Then the matrix equation is discretized and solved to obtain the numerical solutions. Finally, numerical results of viscoelastic string show the effect of the axial tension and axial velocity on its displacement, velocity and acceleration. It also indicates that how dynamic behaviours are affected by external force excitation. In addition, the proposed algorithm shows enormous potentials for solving the problem of high precision dynamics with the variable fractional order model. [ABSTRACT FROM AUTHOR]

Numerical simulation of a two-phase compressible displacement problem is considered in this paper, modelled by a nonlinear system of PDEs. Considering the characters of mathematical model, we present an efficient combination algorithm of the method of characteristics (MOC) and mixed finite volume element (MFVE). The MFVE is used for computing the pressure, Darcy velocity and the saturation. Furthermore, the saturation equation is convection-dominated. MOC eliminates numerical dispersion and nonphysical oscillation, and computes the values at the sharp fronts well. An MFVE-MOC is formed for the saturation. An optimal error estimates in l2 norm is concluded. Finally, numerical examples are given to show the effectiveness and practicability. The composite scheme possibly solves this actual problem well. [ABSTRACT FROM AUTHOR]

Great deluge (GD) algorithm same as other metaheuristics can solve feature selection problem. The GD imitates that in a great deluge someone climbing a hill and attempt to progress in any direction that does not get his/her feet wet in the expectation of discovering a way up when the water Level rises. The drawbacks of GD are: 1) a local search, which may lead the algorithm toward a local optima and 2) a challenging estimation of quality of the final solution in solving most of the problems. In this paper, for the first issue, a population-based great deluge (popGD) algorithm with additional recurrence operation is proposed. This operation is an imitation of no progress of hill climber after a long time; the climber tries to move small steps even downward in hope of finding better way to climb. For the second problem, a technique with an automate alteration of the Level is proposed. The statistical analysis of the results from 25 test functions and 18 benchmark feature selection problems supports the ability of the method. Finally a real-world academician data are employed to perform feature selection and execute classification result with selected features. [ABSTRACT FROM AUTHOR]

The paper considers the design of a multimodal and multilayer inbound logistics network for iron ore to be delivered from suppliers to steel plants. To make cost-efficient logistics and transportation planning decisions, steel companies should account for uncertainty in the demand for iron ore and the economies of scale during transshipment process in the port, which are two critical elements affecting decisions. To this end, we propose a two-stage nonlinear stochastic programming model with the first stage determining the choice of the port to perform transshipment operations and the needed capacity, and the second stage selecting transportation modes after demand uncertainty has been realized. To solve this problem, we first reformulate and linearize the model based on a quantity discount policy applied to the transshipment ports, and then, we develop a scenario-based decomposition algorithm. We conduct a case study based on the data of a steel company in China to illustrate the applicability of our proposed model. Moreover, we perform numerical experiments to demonstrate the effectiveness of our algorithm. [ABSTRACT FROM AUTHOR]

In hyperspectral remote sensing, the classification of hyperspectral imagery is an important issue of concern. However, obtaining sufficient labelled samples for the classification is hard work and consumes enormous labour and material resources. To solve this problem, many scholars make their efforts to the semi-supervised learning method. The self-training model is a popular semi-supervised learning method, which trains a classifier using a few labelled samples and many unlabelled samples in an iterative manner. Nevertheless, the self-training model may provide misclassification as adding incorrect unlabelled samples. This paper proposes a novel semi-supervised learning method, which attempts to introduce the affinity propagation and spatial constraint to self-training model. In the proposed algorithm, a self-training model is employed to expand the labelled sample set. The affinity propagation is applied to select a group of reliable unlabelled samples. To further protect the reliability of unlabelled samples, the selection process of self-training model is constrained in the spatial local area of the labelled samples. In the iteration, the reliable unlabelled samples are selected and added to the labelled sample set. After that, the classifier is trained by the updated labelled samples. The algorithm finishes as the iterations exceed the predetermined value or the labelled sample set is unchanged. Different from the traditional self-training-based semi-supervised learning method, there are mainly three improvements. First, the selection of reliable unlabelled samples is conducted by the affinity propagation, which can effectively improve the reliability of the unlabelled samples. Second, the spatial constraint is introduced to restrict the selection process of self-training model, which can protect the reliability of unlabelled samples and alleviate the computational complexity. Finally, the spectral correlation angle is applied to construct the similarity matrix of affinity propagation, so that the algorithm is more suitable for hyperspectral imagery. A comparative analysis was conducted with classical self-training semi-supervised algorithms to test the effectiveness of the method. It was found that the proposed method provided higher overall accuracy, average accuracy and kappa coefficient (κ) than the competitors. [ABSTRACT FROM AUTHOR]