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.
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