%0 Book Section
%T Fully inverse parametric linear/quadratic programming problems via convex liftings
%+ CentraleSupélec
%+ Laboratoire des signaux et systèmes (L2S)
%+ Dynamical Interconnected Systems in COmplex Environments (DISCO)
%+ Norwegian University of Science and Technology [Trondheim] (NTNU)
%+ Department of Automatic Control and Systems Engineering [Bucharest]
%A Anh Nguyen, Ngoc
%A Olaru, Sorin
%A Rodriguez-Ayerbe, Pedro
%A Hovd, Morten
%A Ion, Necoara
%B Developments in Model-Based Optimization and Control
%V 464
%P 27-47
%8 2015
%D 2015
%K Parametric convex programming problems Convex liftings Inverse parametric convex programming Continuous piecewise affine functions
%Z Engineering Sciences [physics]
%Z Engineering Sciences [physics]/AutomaticBook sections
%X n this chapter, we present in an unified manner the latest developments on inverse optimality problem for continuous piecewise affine (PWA) functions. A particular attention is given to convex liftings as a cornerstone for the constructive solution we advocate in this framework. Subsequently, an algorithm based on convex lifting is presented for recovering a continuous PWA function defined over a polyhedral partition of a polyhedron. We also prove that any continuous PWA function can be equivalently obtained by a parametric linear programming problem with at most one auxiliary one-dimensional variable.
%G English
%L hal-01259951
%U https://centralesupelec.hal.science/hal-01259951
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%~ UNIV-PSUD
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%~ SUP_AUTO
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%~ SUP_SYSTEMES
%~ TESTALAIN1
%~ CENTRALESUPELEC
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%~ TDS-MACS
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%~ UNIV-PSUD-SACLAY
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