Accelerated First-Order Methods for Hyperbolic Programming

TL;DR

This paper introduces a framework that applies accelerated first-order methods to hyperbolic programming, enabling efficient solutions for various convex optimization problems including linear, second-order cone, and semidefinite programming.

Contribution

It develops a general approach to accelerate first-order methods for hyperbolic programming by transforming problems into a convex form with explicit smooth objectives.

Findings

Derived iteration bounds for accelerated methods

Unified approach for multiple types of hyperbolic programs

Applicable to a wide range of convex optimization problems

Abstract

A framework is developed for applying accelerated methods to general hyperbolic programming, including linear, second-order cone, and semidefinite programming as special cases. The approach replaces a hyperbolic program with a convex optimization problem whose smooth objective function is explicit, and for which the only constraints are linear equations (one more linear equation than for the original problem). Virtually any first-order method can be applied. Iteration bounds for a representative accelerated method are derived.