A Strict Complementarity Approach to Error Bound and Sensitivity of Solution of Conic Programs

TL;DR

This paper introduces a geometric framework based on strict complementarity to analyze error bounds and solution sensitivity in conic programming, unifying approaches for LP, SOCP, and SDP.

Contribution

It presents a new, elementary geometric framework that unifies the analysis of error bounds and sensitivity across various conic programs.

Findings

Derived error bounds for LP, SOCP, and SDP.

Provided a geometric interpretation of solution sensitivity.

Unified analysis method for different conic programs.

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).