Exterior point methods with adaptation of admissible set approximation for constrained optimization problems

Abstract

In this paper we consider one approach implemented for solving constrained optimization problems with a given accuracy based on the use of approximation of the admissible set. This approach is applicable to the suquential unconstrained minimization methods, but can be adapted to other optimization methods. At each iteration of the algorithm, designed on this approach, the admissible set of the problem is replaced by its approximation. As a result of the adaptation parameters of approximation in finitely many iterations used approximation becomes satisfactory that guarantees the given accuracy of solution for the initial optimization problem.