A warmstarting technique for general conic optimization in interior point methods

TL;DR

This paper introduces a new warmstarting technique for interior point methods in conic optimization, using a smoothing operator to efficiently generate better starting points that reduce iterations and computational time.

Contribution

The paper presents a novel smoothing-based warmstarting method that improves initial point quality for interior point algorithms in conic optimization.

Findings

Reduces iteration counts in numerical tests

Decreases computational time effectively

Maintains residuals comparable to pre-smoothing points

Abstract

We propose a novel warmstarting method for primal-dual interior point methods based on a smoothing operator that generates a starting point on the central path from the previous optimum. Compared to traditional approaches that prioritize minimizing infeasibility residuals, our method focuses on maintaining proximity to the central path. Computation of a smoothing operator is efficient and can be parallelized for conic constraints. We also prove that the residual of the smoothed starting point remains comparable to the one before the smoothing step. The numerical tests show that the proposed warmstarting strategy can reduce iteration numbers and computational time effectively across test problems.