Inexact-Restoration Algorithm for constrained optimization

JOSÉ MARIO MARTÍNEZ; ELVIO A. PILOTTA

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS

Springer

Lugar: New York; Año: 2000 vol. 104 p. 135 - 163

0022-3239

We introduce a new model algorithm for solving  nonlinear programming problems. No slack variables are introduced for dealing with inequality constraints. Each iteration of the method proceeds in two phases. In the first phase, feasibility of the current iterate is improved and in second phase the objective function value is reduced in an approximate feasible set. The pointthat results from the second phase is compared with the current point  using a nonsmooth merit function that combines feasibility and optimality. This merit function includes a penalty parameter that changes between different iterations. A suitable updating procedure  for this penalty parameter is included by means of which it can be increased or decreased along different iterations. The conditions for feasibility improvement at the first phase and for optimality improvement at the second phase are mild, and large-scale implementations of the resulting method are possible. We prove that under suitable conditions, that do not include regularity or existence of second derivatives, all the limit points of an infinite sequence generated by the algorithm are feasible, and that a suitable optimality measure can be made as small as desired. The algorithm is implemented and tested against LANCELOT using a set of hard-spheres problems.