A Successive Quadratic Programming Based Feasible Directions Algorithm

Abstract

The two-stage Feasible Directions Algorithm for Nonlinearly Constrained Optimization determines a search direction in two stages.First a descent direction is defined; by modifying it, a feasible descent direction is then obtained. We apply this idea in order to state a new feasible directions algorithm based on a well known method for Nonlinear Programming studied by WILSON, HAN and POWELL.

The Successive Quadratic Programming based Feasible Directions Algorithm defines first a descent direction solving a quadratic program ming problem. This direction may be unfeasible, depending on the curva-ture of the active constraints. In a second stage a feasible search direction is then obtained by solving a modified quadratic programming problem, when only equality constraints are considered. These equality constraints are the active constraints of the first stage problem which were perturbed in order to compensate the curvature of the constraints of the nonlinear problem. Finally it’s performed a line search proce-dure which looks for a decrease of the Lagrangian function without loosing the feasibility. The rate of convergence is superlinear and the procedure avoids Maratos effect. Some numerical tests are presented which were solved in a very efficient way.