On the achievement of the complementary approximate Karush-Kuhn-Tucker conditions and algorithmic applications

Focusing on smooth constrained optimization problems, and inspired by the complementary approximate Karush-Kuhn-Tucker (CAKKT) conditions, this work introduces the weighted complementary Approximate Karush-Kuhn-Tucker (WCAKKT) conditions. They are shown to be verified not only by safeguarded augmented Lagrangian methods, but also by inexact restoration methods, inverse and logarithmic barrier methods, and a penalized algorithm for constrained … Read more

A novel sequential optimality condition for smooth constrained optimization and algorithmic consequences

In the smooth constrained optimization setting, this work introduces the Domain Complementary Approximate Karush-Kuhn-Tucker (DCAKKT) condition, inspired by a sequential optimality condition recently devised for nonsmooth constrained optimization problems. It is shown that the augmented Lagrangian method can generate limit points satisfying DCAKKT, and it is proved that such a condition is not related to … Read more

Improving the global convergence of Inexact Restoration methods for constrained optimization problems

Inexact restoration (IR) methods are an important family of numerical methods for solving constrained optimization problems, with applications to electronic structures and bilevel programming, among others areas. In these methods, the minimization is separated into two phases: decreasing infeasibility (feasibility phase) and improving solution (optimality phase). The feasibility phase does not require the generated points … Read more