We consider Karush-Kuhn-Tucker (KKT) systems, which depend on a parameter. Our contribution concerns with the existence of solution of the directionally perturbed KKT system, approximating the given primal-dual base solution. To our knowledge, we give the first explicit result of this kind in...

We present a local convergence analysis of the method of multipliers for equality-constrained variational problems (in the special case of optimization, also called the augmented Lagrangian method) under the sole assumption that the dual starting point is close to a noncritical Lagrange...

<Para ID="Par1">We discuss a certain special subset of Lagrange multipliers, called critical, which usually exist when multipliers associated to a given solution are not unique. This kind of multipliers appear to be important for a number of reasons, some understood better, some (currently) not fully. What is...</para>

Mathematical programs with vanishing constraints constitute a new class of difficult optimization problems with important applications in optimal topology design of mechanical structures. Vanishing constraints usually violate standard constraint qualifications, which gives rise to serious...

In the context of complementarity problems, various concepts of solution regularity are known, each of them playing a certain role in the related theoretical and algorithmic developments. Despite the existence of rich literature on this subject, it appears that the exact relations between some...