Convergence of discrete approximations to optimization problems of neutral functional–differential inclusions

• Published in: Applied mathematics and computation Vol. 165; no. 2; pp. 375 - 391
• Main Author: Wang, Lianwen
• Format: Journal Article
• Language: English
• Published: New York, NY Elsevier Inc 15.06.2005; Elsevier
• Subjects: Calculus of variations and optimal control; Convergence; Discrete approximations; Exact sciences and technology; Finite differences and functional equations; Mathematical analysis; Mathematics; Neutral functional–differential inclusions; Numerical analysis; Numerical analysis. Scientific computation; Numerical methods in mathematical programming, optimization and calculus of variations; Numerical methods in optimization and calculus of variations; Optimization problems; Sciences and techniques of general use; Discrete approximations; Optimization problems; Neutral functional–differential inclusions; Convergence; Strong convergence; Neutral functional-differential inclusions; Optimization method; Strong solution; Algorithm; Euler scheme; Discrete scheme; Numerical approximation; Numerical analysis; Applied mathematics; Optimal solution; Neutral inclusion; Differential inclusion; Finite difference method
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2004.06.018

This paper deals with the convergence of discrete approximations to the optimization problem ( P) for a neutral functional–differential inclusion subject to general endpoint constraints. In the first part of the paper, discrete approximations to the neutral functional–differential inclusion are constructed using Euler finite difference methods and the convergence of discrete approximations is proved. In the second part of the paper, a family of discrete optimization problems ( P N ) to ( P) is provided and the strong convergence of optimal solutions for ( P N ) to the optimal solution of ( P) is discussed.