Inverse parametric linear/quadratic programming problem for continuous PWA functions defined on polyhedral partitions of polyhedra

Ngoc Anh Nguyen 1 Sorin Olaru 1, 2 Pedro Rodriguez-Ayerbe 1
2 DISCO - Dynamical Interconnected Systems in COmplex Environments
L2S - Laboratoire des signaux et systèmes, Inria Saclay - Ile de France, SUPELEC, CNRS - Centre National de la Recherche Scientifique : UMR8506
Abstract : — Constructive solution to inverse parametric lin-ear/quadratic programming problems has recently been investigated and shown to be solvable via convex liftings [15], [14]. These results were stated and solved starting from polytopic partitions of a polytope in the parameter space. Therefore, the case of polyhedral partitions of unbounded polyhedra, was not handled by this method and deserves a complete characterization to address the general inverse optimality problem. This paper has as main objective to overcome the unboundedness limitation of the given polyhedral partition and to extend the constructive solution put forward in [14] for this omitted case.
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Ngoc Anh Nguyen, Sorin Olaru, Pedro Rodriguez-Ayerbe. Inverse parametric linear/quadratic programming problem for continuous PWA functions defined on polyhedral partitions of polyhedra. 54th IEEE Conference on Decision and Control (CDC), Dec 2015, OSAKA, Japan. pp.5926-5931, ⟨10.1109/CDC.2015.7403150⟩. ⟨hal-01334079⟩

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