23 mayo, 2018
12:30 pma1:30 pm

Speaker: Jan J. Rückmann

Title: “Mathematical Programs with Complementarity constraints: Critical Point Theory”

Coauthors: Hubertus Th. Jongen and Vladimir Shikhman.

Date: 23 May.  12:30 h.

Localication: Sala de Seminarios (Edificio Torretamarit)

Abstract. 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.
The lecture is based on a joint paper with Hubertus Th. Jongen and Vladimir Shikhman.