APPLICATION OF THE MODIFIED BARRIER METHOD IN LARGE-SCALE QUADRATIC-PROGRAMMING PROBLEMS

In this paper we present the application of the Penalty/Modified Barri er Function method (PE/MBF) in the solution of large-scale Quadratic P rogramming problems (QP). A review of the recent literature on PE/MBF methods is presented and the choice of this method for QP problems is justified by previous experience in very large-scale bound-constrained problems. The proposed algorithm performs two types of iterations: an outer iteration in which the Lagrange multipliers of the bounds are a djusted, and an inner iteration for the solution of an equality constr ained subproblem. The inner iteration solves a modified problem, conta ining penalty/modified barrier terms for the bounds in the objective a nd is subject to equality constraints only. The equality constraints a re handled directly via the use of additional Lagrange multipliers dur ing the inner iteration and thus, instead of an unconstrained problem, the inner iteration solves a modified equality constrained problem. A ny inequality constraints, other than bounds, are formulated as equali ties via the use of slack variables. Computational results show this m ethod to be promising, and motivate further investigation for the gene ral case of nonlinear programming problems.