Strong Duality Theorem for Continuous-Time Linear Programming Problems

TL;DR

This paper proves a strong duality theorem for continuous-time linear programming problems with general discontinuities, extending previous results by introducing new discretized primal and dual problems.

Contribution

It introduces a novel approach with different discretizations to establish strong duality for problems with arbitrary discontinuities.

Findings

Proved strong duality theorem for general discontinuous coefficients.

Developed new discretized primal and dual problems.

Extended previous results to broader class of problems.

Abstract

This paper is aimed to prove the strong duality theorem for continuous-time linear programming problems in which the coefficients are assumed to be piecewise continuous functions. The previous paper proved the strong duality theorem for the case of piecewise continuous functions in which the discontinuities are the left-continuities. In this paper, we propose the completely different type of discretized primal and dual problems that can be used to prove the strong duality theorem for the general situation of discontinuities.