Two error bounds for constrained optimization problems and their applications
The trust region method is a popular method for solving constrained optimization problem and there is a lot of literature about it. The aim of this paper is to study a global error bound for the projected gradient and a local error bound for the distance from a feasible solution to the optimal solution set of a nonlinear programming problem by using some characteristic quantities such as value function, trust region radius etc., which appeared in the trust region method. As applications of these error bounds, the authors obtain sufficient conditions under which a sequence of feasible solutions converges to a stationary point or to an optimal solution , respectively, and a necessary and sufficient condition under which a sequence of feasible solutions converges to a Kuhn-Tucker point. Other applications involve finite termination of a sequence of feasible solutions. For general optimization problems, when the optimal solution set is generalized non-degenerate or gives generalized weak sharp minima, the authors give a necessary and sufficient condition for a sequence of feasible solutions to terminate finitely at a Kuhn-Tucker point, and a sufficient condition which guarantees that a sequence of feasible solutions terminates finitely at a stationary point.
scientific article; zbMATH DE number 5562554
scientific article