A Strict Complementarity Approach to Error Bound and Sensitivity of Solution of Conic Programs
Optimization and Control
2022-09-19 v2
Abstract
In this paper, we provide an elementary, geometric, and unified framework to analyze conic programs that we call the strict complementarity approach. This framework allows us to establish error bounds and quantify the sensitivity of the solution. The framework uses three classical ideas from convex geometry and linear algebra: linear regularity of convex sets, facial reduction, and orthogonal decomposition. We show how to use this framework to derive error bounds for linear programming (LP), second order cone programming (SOCP), and semidefinite programming (SDP).
Cite
@article{arxiv.2012.00183,
title = {A Strict Complementarity Approach to Error Bound and Sensitivity of Solution of Conic Programs},
author = {Lijun Ding and Madeleine Udell},
journal= {arXiv preprint arXiv:2012.00183},
year = {2022}
}
Comments
23 pages, 2 figures. In this revision, we added an approach based on conic decomposition. See Section D for details