THE MODIFIED BARRIER FUNCTION-APPROACH FOR LARGE-SCALE OPTIMIZATION

This paper studies the modified barrier function approach for large-sc ale nonlinear constrained optimization. Following a review of the rece nt literature on modified barrier function approaches for nonlinear op timization, the steps of a proposed algorithm are examined in full det ail. The basic steps of this algorithm comprise an outer iteration, in which the Lagrange multipliers and various penalty parameters are upd ated, and an inner iteration, in which an unconstrained nonlinear opti mization problem is solved. The algorithm presented has been implement ed in a general-purpose routine which is denoted as MBFSOL. Numerical results are presented for a variety of problems, from small to very la rge-scale. The examples show the effectiveness of the algorithm in ver y large problems, particularly in bound constrained case studies of up to many thousands of variables and severe ill-conditioning. (C) 1997 Elsevier Science Ltd.