Local models in equilibrium optimization
Dominik Dorsch, Hubertus Th. Jongen, Vladimir Shikhman · Digital Access to Libraries (Université catholique de Louvain (UCL), l'Université de Namur (UNamur) and the Université Saint-Louis (USL-B)) · 2013
We study equilibrium optimization from a structural point of view. For that, we consider equilibrium optimization problems up to smooth local coordinate transformations at their solutions. The latter equivalence relation induces classes of equilibrium optimization problems. We focus on stable classes corresponding to a dense set of data functions. We prove that these classes are unique and call them "basic classes". Their representatives in the simplest form are called local models. For particular realizations of equilibrium optimization basic classes and their local models are elaborated. The latter include bilevel optimization, general semi-infinite programming and Nash optimization. In bilevel optimization we discuss new phenomena arising from the appearance of multiple global minimizers as well as their possible bifurcation.