Any discontinuous PWA function is optimal solution to a parametric linear programming problem

Ngoc Anh Nguyen 1 S Olaru 2, 1 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 : Recent studies have investigated the continuous functions in terms of inverse optimality. The continuity is a primordial structural property which is exploited in order to link a given piecewise affine (PWA) function to an optimization problem. The aim of this work is to deepen the study of the PWA functions in the inverse optimality context and specifically deal with the presence of discontinuities. First, it will be shown that a solution to the inverse optimality problem exists via a constructive argument. The loss of continuity will have an implication on the structure of the optimization problem which, albeit convex, turns to have a set-valued optimal solution. As a consequence, the original PWA function will represent an optimal solution but the uniqueness is lost. From the numerical point of view, we introduce an algorithm to construct an optimization problem that admits a given discontinuous PWA function as an optimal solution. This construction is shown to rely on convex liftings. A numerical example is considered to illustrate the proposal.
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Communication dans un congrès
54th IEEE Conference on Decision and Control (CDC 2015), Dec 2015, Osaka, Japan. 2015 IEEE 54th Annual Conference on Decision and Control (CDC), pp.5926-5931, 2015, 〈10.1109/CDC.2015.7403151〉
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Dernière modification le : jeudi 5 avril 2018 - 12:30:13
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Ngoc Anh Nguyen, S Olaru, Pedro Rodriguez-Ayerbe. Any discontinuous PWA function is optimal solution to a parametric linear programming problem. 54th IEEE Conference on Decision and Control (CDC 2015), Dec 2015, Osaka, Japan. 2015 IEEE 54th Annual Conference on Decision and Control (CDC), pp.5926-5931, 2015, 〈10.1109/CDC.2015.7403151〉. 〈hal-01367123〉

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