A Nonmonotone Trust Region-Line Search Exact Penalty Projected Hessian Algorithm for Constrained Nonlinear Optimization

We present a nonmonotone combined trust region-line search exact penalty algorithm for solving general constrained nonlinear optimization problems. Iterations of the algorithm are partitioned into “infeasible”, “almost feasible” and “local” iterations. In an infeasible iteration, either a possible infeasible stationary point is detected or the penalty parameter is updated so that approach to the feasible region is guaranteed. In an almost feasible iteration, a horizontal step direction is computed to reduce the objective function and a vertical step direction is calculated to maintain the feasibility. In a local iteration, the Lagrange multipliers are computed by solving a linear least squares problem. If the computed Lagrange multipliers satisfy the first order optimality conditions, a Newton step direction is computed. Otherwise, a dropping step is calculated which as a descent direction for the penalty function. We also use a new nonmonotone strategy for evaluating the step directions and updating the iterates. We implement the algorithm in the MATLAB environment. The preliminary numerical experiments on some test problems confirm the efficiency of the proposed algorithm.

Keywords:

Constrained Optimization , Exact Penalty Function , Trust Region , Line Search , Inexact Methods , BFGS Update