Ching-Feng Wen

On a recurrence algorithm for continuous-time linear fractional programming problems

In this paper, we develop a discrete approximation method for solving continuous-time linear fractional programming problems. Our method enables one to derive a recurrence structure which shall overcome the computational curse caused by the increasing numbers of decision variables in the approximate decision problems when the subintervals are getting smaller and smaller. Furthermore, our algorithm provides estimation for the error bounds of the approximate solutions. We also establish the convergence of our approximate solutions to the continuous-time linear fractional programming problems. Numerical examples are provided to illustrate the quality of the approximate solutions.

On general systems of variational inequalities

In this paper, we present a new relaxed viscosity approximation method, and prove the strong convergence of the method to a common fixed point of finitely many nonexpansive mappings and a strict pseudocontraction that also solves a suitable equilibrium problem and a general system of variational inequalities.

Approximate solutions and error bounds for a class of continuous-time linear programming problems

In this article, we discuss a class of continuous-time linear programming (CLP) problems. We provide a discrete approximation procedure to find numerical solutions of CLP, establish the estimation for the error bound and prove that the searched sequence of approximate solution functions weakly star converges to an optimal solution of CLP. Finally, we provide some numerical examples to implement our proposed method and to show the quality of the proposed error bound.

Generalized viscosity implicit rules for solving quasi-inclusion problems of accretive operators in Banach spaces

The generalized viscosity implicit rules for solving quasi-inclusion problems of accretive operators in Banach spaces are established. The strong convergence theorems of the rules to a solution of quasi-inclusion problems of accretive operators are proved under certain assumptions imposed on the sequences of parameters. The results presented in this paper extend and improve the main results of Refs. (Moudafi, J Math Anal Appl. 2000;241:46–55; Xu et al., Fixed Point Theory Appl. 2015;2015:41; López et al., Abstr Appl Anal. 2012;2012; Cholamjiak, Numer Algor. DOI:10.1007/s11075-015-0030-6.). Moreover, some applications to monotone variational inequalities, convex minimization problem and convexly constrained linear inverse problem are presented.

Some Modified Extragradient Methods for Solving Split Feasibility and Fixed Point Problems

We consider and study the modified extragradient methods for finding a common element of the solution set of a split feasibility problem (SFP) and the fixed point set of a strictly pseudocontractive mapping in the setting of infinite-dimensional Hilbert spaces. We propose an extragradient algorithm for finding an element of where is strictly pseudocontractive. It is proven that the sequences generated by the proposed algorithm converge weakly to an element of . We also propose another extragradient-like algorithm for finding an element of where is nonexpansive. It is shown that the sequences generated by the proposed algorithm converge strongly to an element of .

Common zero point for a finite family of inclusion problems of accretive mappings in Banach spaces

Abstract The purpose of this article is to propose a splitting algorithm for finding a common zero of a finite family of inclusion problems of accretive operators in Banach space. Under suitable conditions, some strong convergence theorems of the sequence generalized by the algorithm to a common zero of the inclusion problems are proved. Some applications to the convex minimization problem, common fixed point problem of a finite family of pseudocontractive mappings, and accretive variational inequality problem in Banach spaces are presented.

The modified proximal point algorithm in Hadamard spaces

The purpose of this paper is to propose a modified proximal point algorithm for solving minimization problems in Hadamard spaces. We then prove that the sequence generated by the algorithm converges strongly (convergence in metric) to a minimizer of convex objective functions. The results extend several results in Hilbert spaces, Hadamard manifolds and non-positive curvature metric spaces.

On Some Properties of Parametric Quadratic Programs Pertaining to Continuous-time Quadratic Fractional Programming

This article is concerned with quadratic fractional optimal control problems with linear state constraints. Such problems are called the {\em continuous-time quadratic fractional programming problems} (CQFP). Some basic properties of parametric continuous-time quadratic programming problems pertaining to (CQFP) are derived. By these properties, (CQFP) can be reduced to continuous-time quadratic programming problems. Besides, a discretization approach for solving continuous-time quadratic programming problems is also developed. The developed approach will provide an important foundation for constructing a parametric computational procedure for (CQFP).

A numerical method for solving a class of continuous-time linear programming problems

In this paper, we discuss a class of continuous- time linear programming problems (CLP) posed in a function space. A practical and simple method for finding approximate solutions of (CLP) is presented. The convergence proof is provided for the proposed scheme. By our constructive manner the error bound of every approximate value can be estimated as well.

A modified viscosity implicit-type proximal point algorithm for monotone inclusions and asymptotically nonexpansive mappings in Hadamard spaces

The purpose of this article is to propose a modified viscosity implicit-type proximal point algorithm for approximating a common solution of a monotone inclusion problem and a fixed point problem for an asymptotically nonexpansive mapping in Hadamard spaces. Under suitable conditions, some strong convergence theorems of the proposed algorithms to such a common solution are proved. Our results extend and complement some recent results in this direction.