Random projections for conic programs

TL;DR

This paper explores how random projections can be applied to conic programming problems, providing theoretical approximation guarantees and demonstrating practical effectiveness through computational experiments.

Contribution

It introduces a novel framework using Jordan algebras for analyzing random projections in conic programs, with both theoretical and experimental insights.

Findings

Random projections preserve feasibility with high probability.

Approximate solutions can be efficiently obtained via projections.

Experimental results support practical applicability.

Abstract

We discuss the application of random projections to conic programming: notably linear, second-order and semidefinite programs. We prove general approximation results on feasibility and optimality using the framework of formally real Jordan algebras. We then discuss some computational experiments on randomly generated semidefinite programs in order to illustrate the practical applicability of our ideas