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

The application of the penalty/modified barrier function method (PE/MB F) is presented for the solution of large-scale positive-semidefinite quadratic programming problems (QP). A review of the recent literature on QP methods is presented and the choice of the PE/MBF method for QP problems is justified by previous experience in very large-scale boun d-constrained problems. The proposed algorithm performs two types of i terations: an outer iteration in which the Lagrange multipliers of the bounds are adjusted, and an inner iteration for the solution of an eq uality constrained subproblem. The inner iteration solves a modified p roblem, containing penalty/modified barrier terms for the bounds in th e objective, and is subject to equality constraints only. The equality constraints are handled directly via the use of additional Lagrange m ultipliers during the inner iteration and thus, instead of an unconstr ained problem, the inner iteration solves a modified equality constrai ned problem. Any inequality constraints, other than bounds, are formul ated as equalities via the use of slack variables. Computational resul ts show this method to be promising, and motivate further investigatio n for the general case of nonlinear programming problems. (C) 1998 Els evier Science Ltd. All rights reserved.