Gemayqzel Bouza Allende

Solving bilevel programs with the KKT-approach

Bilevel programs (BL) form a special class of optimization problems. They appear in many models in economics, game theory and mathematical physics. BL programs show a more complicated structure than standard finite problems. We study the so-called KKT-approach for solving bilevel problems, where the lower level minimality condition is replaced by the KKT- or the FJ-condition. This leads to a special structured mathematical program with complementarity constraints. We analyze the KKT-approach from a generic viewpoint and reveal the advantages and possible drawbacks of this approach for solving BL problems numerically.

Embedding methods for solving variational inequalities

Variational inequality problems (VIP) are an important class of mathematical problems that appear in many practical situations. So, it is important to find efficient and robust numerical solution methods. An appealing idea is to embed the VIP into a one-parametric problem which, then, can be solved numerically by a path-following method. In this article, we study two different types of embeddings and we analyse their generic properties. The non-linear complementarity problem and box-constrained VIP are discussed as special cases.