A Random Active Set Method for Strictly Convex Quadratic Problem with Simple Bounds

TL;DR

This paper introduces a novel random active set method for strictly convex quadratic problems with bounds, ensuring finite convergence probability without extra conditions, and demonstrating improved robustness and efficiency.

Contribution

It proposes a new random active set algorithm that guarantees finite convergence without strict assumptions, enhancing robustness and efficiency over existing methods.

Findings

Converges in finite steps with probability one.

Achieves correct active set in few iterations.

Outperforms existing methods in robustness and efficiency.

Abstract

Active set method aims to find the correct active set of the optimal solution and it is a powerful method for solving strictly convex quadratic problem with bound constraints. To guarantee the finite step convergence, the existing active set methods all need strict conditions or some additional strategies, which greatly affect the efficiency of the algorithm. In this paper, we propose a random active set method which introduces randomness in the update of active set. We prove that it can converge in finite iterations with probability one without any conditions on the problem or any additional strategies. Numerical results show that the algorithm obtains the correct active set within a few iterations, and compared with the existing methods, it has better robustness and efficiency.