Leonardo D. Secchin

Bilevel optimization with a multiobjective problem in the lower level

Categories Constrained Nonlinear Optimization, Multi-Criteria Optimization

Bilevel problems model instances with a hierarchical structure. Aiming at an efficient solution of a constrained multiobjective problem according with some pre-defined criterion, we reformulate this optimization but non standard problem as a classic bilevel one. This reformulation intents to encompass all the objectives, so that the properly efficient solution set is recovered by means … Read more

Convergence properties of a second order augmented Lagrangian method for mathematical programs with complementarity constraints

Categories Complementarity and Variational Inequalities Tags , ,

Mathematical Programs with Complementarity Constraints (MPCCs) are difficult optimization problems that do not satisfy the majority of the usual constraint qualifications (CQs) for standard nonlinear optimization. Despite this fact, classical methods behaves well when applied to MPCCs. Recently, Izmailov, Solodov and Uskov proved that first order augmented Lagrangian methods, under a natural adaption of the … Read more