A New Pivot Selection Algorithm for Symmetric Indefinite Factorization Arising in Quadratic Programming with Block Constraint Matrices

TL;DR

This paper introduces a new pivot selection algorithm for symmetric indefinite factorization in quadratic programming with block diagonal constraints, improving sparsity and stability.

Contribution

The paper proposes a novel pivot selection algorithm for KKT matrix factorization that reduces fill-ins and enhances sparsity compared to existing methods.

Findings

No fill-ins in factorization with the new algorithm

Factors are sparser than those produced by MA57

Maintains sparsity and stability in quadratic programming solutions

Abstract

Quadratic programmingis a class of constrained optimization problem with quadratic objective functions and linear constraints. It has applications in many areas and is also used to solve nonlinear optimization problems. This article focuses on the equality constrained quadratic programs whose constraint matrices are block diagonal. Using the direct solution method, we propose a new pivot selection algorithm for the factorization of the Karush-Kuhn-Tucker(KKT) matrix for this problem that maintains the sparsity and stability of the problem. Our experiments show that our pivot selection algorithm appears to produce no fill-ins in the factorizationof such matrices. In addition, we compare our method with MA57 and find that the factors produced by our algorithm are sparser.