Mariana da Rosa In this paper we consider an augmented Lagrangian method with general lower-level constraints, that is, where some of the constraints are penalized while others are kept as subproblem constraints. Motivated by some recent results on optimization problems on manifolds, we present a general theory of global convergence when a feasible approximate KKT point is found … Read more
In this paper, we analyze augmented Lagrangian (AL) methods for mathematical programs with complementarity constraints (MPCCs), with emphasis on a variant that reformulates the complementarity constraints by slack variables and preserves them explicitly in the subproblems instead of penalizing them. Motivated by recent developments in nonlinear programming, we study quasi-normality-type constraint qualifications tailored to this … Read more
Constraint qualifications (CQs) are fundamental for understanding the geometry of feasible sets and for ensuring the validity of optimality conditions in nonlinear programming. A known idea is that constant-rank type CQs allow one to modify the description of the feasible set, by eliminating redundant constraints, so that the Mangasarian-Fromovitz CQ (MFCQ) holds. Traditionally, such modifications, … Read more