Projection methods in conic optimization

TL;DR

This paper reviews algorithms for projecting points onto convex cones intersected with affine subspaces, highlighting regularization methods in conic and polynomial optimization with applications across various fields.

Contribution

It provides a comprehensive overview of recent algorithms for conic projections, emphasizing regularization techniques and their applications in polynomial optimization.

Findings

Efficient algorithms for conic projections are crucial in optimization.

Regularization algorithms enhance solution methods for linear conic problems.

Applications span science, finance, and engineering.

Abstract

There exist efficient algorithms to project a point onto the intersection of a convex cone and an affine subspace. Those conic projections are in turn the work-horse of a range of algorithms in conic optimization, having a variety of applications in science, finance and engineering. This chapter reviews some of these algorithms, emphasizing the so-called regularization algorithms for linear conic optimization, and applications in polynomial optimization. This is a presentation of the material of several recent research articles; we aim here at clarifying the ideas, presenting them in a general framework, and pointing out important techniques.