On Solving a Class of Linear Semi-Infinite Programs by the Trigonometric Moment

TL;DR

This paper introduces a new practical method for solving a specific class of semi-infinite programs using trigonometric moments, achieving near-optimal solutions with demonstrated numerical efficiency.

Contribution

The paper develops an easily implementable approach that constructs approximate linear semidefinite programs based on duality and trigonometric moments, providing near-optimal solutions.

Findings

Achieves lnK/K-optimal solutions for semi-infinite programs

Demonstrates numerical efficiency through examples

Provides a practical method for a class of semi-infinite programs

Abstract

In this paper, we propose a new easily implementable method for solving a class of semi-infinite programs, where an approximate linear semidefinite program is constructed for the concerned semi-infinite program based on the duality theory of semi-infinite programs and the theory of the trigonometric moments. We obtain a lnK/K-optimal solution for the semi-infinite program, where K is the truncation factor. Moreover, we present some numerical examples to show the efficiency of the new method.