CONFERENCIA

  Computation of graphical derivative of solution maps in parameterized equilibria with conic constraints

         Doc. Ing. Jiří Outrata, DrSc.

Institute of Information Theory and Automation,

Czech Academy of Sciences

República Checa

Fecha: Miércoles 5 de febrero de 2014

Hora:   12:30

Lugar: Sala de seminarios, Edificio Torretamarit

Resumen:

The lecture deals with the computation of the graphical derivative of the solution map in a parameterized generalized equation with a conic constraint set (given as the pre-image of a closed convex cone). Under standard reducibility and nondegeneracy assumptions we compute in the first step the directional derivative of the metric projection onto the constraint set at points, sufficiently close to the reference value of the decision variable. On the basis of this result we are then able to obtain a formula for the desired graphical derivative, provided either the constraint set is convex or fully amenable. In the later situation we make use of an important result concerning the relationship between the projection operator and the (limiting) normal-cone mapping. The obtained graphical derivative formula can be employed in a workable criterion (or even characterization) of the isolated calmness of the solution map which is a valuable stability property. The results are illustrated by simple academic examples involving the ice cream cone

Key words. Variational Analysis, graphical derivatives, generalized equations, conic programming.

Jiří Outrata es investigador del Instituto de Teoría de la Información y Automatización de la Academia Checa de las Ciencias. Es autor de 3 monografías y más de 70 publicaciones en revistas, siendo editor asociado de SIAM Journal on Optimization, Set-Valued and Variational Analysys, y Kybernetika. Es un referente reconocido internacionalmente en las áreas de optimización y análisis variacional y, entre otras distinciones, desde 2013 es Profesor Adjunto de la Escuela de Teoría de la Información y Ciencias Matemáticas de la Universidad de Ballarat en Australia.