Mathematical Programs with Complementarity constraints: Critical Point Theory

Título: Mathematical Programs with Complementarity constraints: Critical Point Theory

Ponente: Jan J. Rückmann (Universidad de Bergen, Noruega)

Fecha: Miércoles 23 de mayo de 2018 a las 12:30 horas

Lugar: Sala de Seminarios,  Instituto Universitario de Investigación CIO, Edificio Torretamarit, Universidad Miguel Hernández (Campus de Elche)

Resumen:

We study mathematical programs with complementarity constraints from a topological point of view. We derive a Morse Lemma at nondegenerate C-stationary points and present two basic theorems from Morse theory (deformation theorem and cell-attachment theorem). Outside the C-stationary point set,continuous deformation of lower level sets can be performed and, as a consequence, the topological data (such as the number of connected components) remain invariant. However, when passing a level containing a C-stationary point, the topology of the lower level set changes via the attachment of a q-dimensional cell where its dimension equals the stationary C-index of the corresponding C-stationary point. The stationary C-index depends on both the restricted Hessian of the Lagrangian and the Lagrange multipliers related to bi-active complementarity constraints. Finally, some relations with other stationarity concepts are discussed.