A Penalty-free Method With Two-side Reduced Hesse For Constrained Optimization

We use various penalty functions usually to solve nonlinear equality constrainedoptimization problems, which are called the penalty-type methods, but the choice ofpenalty parameter may cause lots of trouble. Indeed, the biggish penalty parametermay cause an ill-conditioned problem numerically. Therefore, it is very important todevise some penalty-free method. Filter technique, which is presented by Fletcher etal in1997, is so far the most classical penalty-free method with satisfactory numericalefect. Filter methods need to retain a flter set at the every iterate point, which maycause a bigger storage. Therefore, the research in penalty-free method without fltertechnique is of great value in theory and practice.In this paper, we propose a class of new penalty-free method, which has no choiceof penalty function and no flter technique, to solve nonlinear programming with non-linear equality constraints. In order to deal with large scale problems, we use linesearch procedures and two-sided projected Hessian method in the algorithm and pro-gressively decrease objective function value within the measure of feasibility to enforcethe algorithm to get the optimal solution. Under usual assumptions, we analyze theglobal convergence of the algorithm presented. In order to prevent the Maratos ef-fect, we employ second order correction steps and analyze the local convergence ofthe algorithm with second order correction under mild conditions. Finally, we testthe problems in CUTEr which is constrained and unconstrained testing enviromentrecognized internationally. The numerical results shows that the algorithm is efcient.