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

arXiv: https://arxiv.org/abs/2012.00183 · HTML: https://mlsanity.com/paper/2012.00183/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Dec 2020.

## Built on by (most cited first, 1 of 1)

- [dOPT: Differentiating Conic Optimization via Geometric Reduction](https://mlsanity.com/paper/2609.33828/) (2026)

## Abstract (arXiv)

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).