A Constraint-Reduced MPC Algorithm for Convex Quadratic Programming, with a Modified Active Set Identification Scheme

TL;DR

This paper introduces a constraint-reduced Mehrotra-Predictor-Corrector algorithm for convex quadratic programming that improves computational efficiency and includes a novel active-set identification scheme, with proven convergence properties.

Contribution

It proposes a new constraint-reduced algorithm with a regularization scheme and a modified active-set identification method, enhancing efficiency and robustness in convex quadratic programming.

Findings

Demonstrates significant CPU savings in numerical tests.

Shows effective active-set identification performance.

Establishes convergence under general conditions.

Abstract

A constraint-reduced Mehrotra-Predictor-Corrector algorithm for convex quadratic programming is proposed. (At each iteration, such algorithms use only a subset of the inequality constraints in constructing the search direction, resulting in CPU savings.) The proposed algorithm makes use of a regularization scheme to cater to cases where the reduced constraint matrix is rank deficient. Global and local convergence properties are established under arbitrary working-set selection rules subject to satisfaction of a general condition. A modified active-set identification scheme that fulfills this condition is introduced. Numerical tests show great promise for the proposed algorithm, in particular for its active-set identification scheme. While the focus of the present paper is on dense systems, application of the main ideas to large sparse systems is briefly discussed.