Multiparametric analysis of conic linear optimization based on the lift-and-project procedure
Abstract
We study how the lift-and-project procedure applies to the multiparametric analysis of conic linear optimization (CLO) problems. We first introduce the concept of a pair of primal and dual conic representable sets and define the set-valued mappings between them. We then explore a novel kind of duality of mpCLOs, which allows us to generalize as well as treat previous results for the mulitparametric analysis in a unified framework. In particular, we discuss the behavior of the optimal partition of a conic representable set. This leads to the invariant region decomposition of a conic representable set that is more general than the known results in the literatures. Finally, we study the properties of the optimal objective values as a function of that parametric vectors. All results are corroborated by examples having correlation.
Cite
@article{arxiv.2006.08104,
title = {Multiparametric analysis of conic linear optimization based on the lift-and-project procedure},
author = {Zi-zong Yan and Xiangjun Li and Jinhai Guo},
journal= {arXiv preprint arXiv:2006.08104},
year = {2022}
}
Comments
34 pages, 3 figure