The prerestorative step in the sequential Gradient-Restoration Algorithm for mathematical Programming problems with inequality constraints*

摘要

In this paper, the problem of minimizing a function of several variables subject to inequality constraints is considered. The method employed is the sequential gradient-restoration algorithm with complete restoration. In this algorithm, the inequality constraints are transformed into equality constraints by suitable transformations. A modification of the sequential gradient-restoration algorithm, designed to improve the convergence characteristics, is presented. It consists of inserting a prerestorative step prior to any iteration of the algorithm. The aim of this prerestorative step is to reduce the constraint violation. Eight numerical examples are presented. They show the considerable beneficial effects associated with the above prerestorative step: on the average, the number of iterations of the modified algorithm is less than 50% of the number of iterations of the standard algorithm. An analogous remark holds for the computer time.