A note on generalized semi-infinite program bounding methods
Optimization and Control
2019-12-04 v1
Abstract
Generalized semi-infinite programs (GSIP) are a class of mathematical optimization problems that generalize semi-infinite programs, which have a finite number of decision variables and infinite constraints. Mitsos et al. (Mitsos and Tsoukalas. "Global optimization of generalized semi-infinite programs via restriction of the right hand side." Journal of Global Optimization 61.1 (2015): 1-17.) present a method for global optimization of GSIP. This method involves a lower bounding method, and they claim that these lower bounds converge to the optimal objective value of the GSIP. A counterexample is presented that shows that this claim is false.
Cite
@article{arxiv.1912.01075,
title = {A note on generalized semi-infinite program bounding methods},
author = {Stuart M. Harwood},
journal= {arXiv preprint arXiv:1912.01075},
year = {2019}
}