A Dual Method for Minimax Quadratic Programming

TL;DR

This paper introduces a dual algorithm for minimax quadratic programming with inequality constraints, transforming the problem into equality constrained subproblems and guaranteeing finite termination with numerical stability.

Contribution

It extends the dual active set method to minimax problems, providing a finite, stable, and efficient algorithm with proven convergence.

Findings

Algorithm terminates in finite steps

Demonstrates high accuracy and stability

Effective on various test problems

Abstract

This paper investigates minimax quadratic programming problems with coupled inequality constraints. By leveraging a duality theorem, we develop a dual algorithm that extends the dual active set method to the minimax setting, transforming the original inequality constrained problem into a sequence of equality constrained subproblems. Under a suitable assumption, we prove that the associated S-pairs do not repeat and that the algorithm terminates in a finite number of iterations, guaranteed by the monotonic decrease of the objective function value. To ensure numerical stability and efficiency, the algorithm is implemented using Cholesky factorization and Givens rotations. Numerical experiments on both randomly generated minimax quadratic programs and illustrative applications demonstrate the accuracy, stability, and computational effectiveness of the proposed algorithm.