Solving Continuous-Time Linear Programming Problems Based on the Piecewise Continuous Functions. (1st September 2016)

• Record Type: Journal Article
• Authors: Wu, Hsien-Chung
• Is Part Of: Numerical functional analysis and optimization. Volume 37:Number 9(2016)
• Page Start: 1168
• Page End: 1201
• Publication Date: 2016-09-01
• Subjects: Continuous-time linear programming problems -- discretized problems -- piecewise continuous functions -- strong duality theorem -- weak duality theorem; 90C05 -- 90C46 -- 90C90; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2016.1193517
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: The numerical method is proposed in this article to solve a general class of continuous-time linear programming problems in which the functions appeared in the coefficients of this problem are assumed to be piecewise continuous. In order to make sure that all the subintervals of time interval will not contain the discontinuities, a different methodology for not equally partitioning the time interval is proposed. The main issue of this article is to obtain an analytic formula of error upper bound. In this article, we shall propose two kinds of computational procedure to evaluate the error upper bounds. One needs to solve the dual problem of the discretized linear programming problem, and another one does not need to solve the dual problem. Finally, we present a numerical example to demonstrate the usefulness of the numerical method.