English

Semidefinite programming relaxations for linear semi-infinite polynomial programming

Optimization and Control 2019-10-25 v4

Abstract

This paper studies a class of so-called linear semi-infinite polynomial programming (LSIPP) problems. It is a subclass of linear semi-infinite programming problems whose constraint functions are polynomials in parameters and index sets are basic semialgebraic sets. We present a hierarchy of semidefinite programming (SDP) relaxations for LSIPP problems. Convergence rate analysis of the SDP relaxations is established based on some existing results. We show how to verify the compactness of feasible sets of LSIPP problems. In the end, we extend the SDP relaxation method to more general semi-infinite programming problems.

Keywords

Cite

@article{arxiv.1509.06394,
  title  = {Semidefinite programming relaxations for linear semi-infinite polynomial programming},
  author = {Feng Guo and Xiaoxia Sun},
  journal= {arXiv preprint arXiv:1509.06394},
  year   = {2019}
}

Comments

22 pages, a revised version according to the comments from the referee

R2 v1 2026-06-22T11:02:07.711Z