Nonasymptotic and asymptotic linear convergence of an almost cyclic SHQP Dykstra's algorithm for polyhedral problems

TL;DR

This paper proves that an almost cyclic Dykstra's algorithm with SHQP strategy converges linearly both in the short term and long term for polyhedral problems, enhancing understanding of its efficiency.

Contribution

It introduces a convergence analysis for an almost cyclic Dykstra's algorithm with SHQP, demonstrating linear convergence rates for polyhedral problems.

Findings

Achieves nonasymptotic linear convergence.

Establishes asymptotic linear convergence.

Applicable to polyhedral optimization problems.

Abstract

We show that an almost cyclic (or generalized Gauss- Seidel) Dykstra's algorithm which incorporates the SHQP (supporting halfspace- quadratic programming) strategy can achieve nonasymptotic and asymptotic linear convergence for polyhedral problems.