%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 %~ CNRS %~ INRIA %~ UNIV-PSUD %~ INRIA-SACLAY %~ SUP_LSS %~ SUP_AUTO %~ INRIA_TEST %~ SUP_SYSTEMES %~ TESTALAIN1 %~ CENTRALESUPELEC %~ INRIA2 %~ TDS-MACS %~ UNIV-PARIS-SACLAY %~ UNIV-PSUD-SACLAY %~ INRIA-SACLAY-2015 %~ CENTRALESUPELEC-SACLAY %~ GS-COMPUTER-SCIENCE %~ DISCO-L2S