The modified barrier function approach for large-scale optimization

Abstract

This paper studies the modified barrier function approach for large-scale nonlinear constrained optimization. Following a review of the recent literature on modified barrier function approaches for nonlinear optimization, the steps of a proposed algorithm are examined in full detail. The basis steps of this algorithm comprise an outer iteration, in which the Lagrange multipliers and various penalty parameters are updated, and an inner iteration, in which an unconstrained nonlinear optimization problem is solved. The algorithm presented has been implemented in a general-purpose routine which is denoted as MBFSOL. Numerical results are presented for a variety of problems, from small to very large-scale. The examples show the effectiveness of the algorithm in very large problems, particularly in bound constrained case studies of up to many thousands of variables and severe illconditioning.