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Type Conference Presentation
Scope Discipline-based scholarship
Title Parametric Optimization and Variational Problems Involving Polyhedral Multifunctions
Organization Unit
Authors
  • Diethard Klatte
Presentation Type lecture
Item Subtype Original Work
Refereed Yes
Status Published in final form
Language
  • English
Event Title Parametric Optimization and Related Topics (Paraopt XI)
Event Type conference
Event Location Prague, Czech Republic
Event Start Date September 19 - 2017
Event End Date September 22 - 2017
Abstract Text A multivalued mapping between finite dimensional spaces is called polyhedral (Robinson 1982) if its graph is the union of finitely many polyhedral convex sets. For example, the optimal solution set mapping of a "canonically perturbed" linear or quadratic program is polyhedral. Similarly, the solution multifunction of an affine variational inequality under suitable parametrization has this property. Polyhedral multifunctions are of particular interest in the stability analysis of the classes of problems just mentioned and are also used in the study of linear inequalities, piecewise linear equations, complementarity problems, disjunctive optimization and many other subjects. The pioneering work in the 1970ies of F. Nozicka (a founder of the series of "Paraopt" conferences) on parametric linear optimization is one of the fundamentals for this theory. In our talk, we present characterizations and applications of several types of Lipschitz properties (e.g., upper Lipschitz behavior, metric regularity, strong regularity) for optimization and variational problems involving a polyhedral structure. We cover both classical and more recent developments on this topic. In particular, we show how to apply results from variational analysis to the classes of problems under consideration. This talk benefits from the cooperation with Bernd Kummer, Humboldt University Berlin.
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