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Fully inverse parametric linear/quadratic programming problems via convex liftings

Abstract : 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.
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Submitted on : Thursday, January 21, 2016 - 12:12:32 PM
Last modification on : Wednesday, April 8, 2020 - 6:28:02 PM

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  • HAL Id : hal-01259951, version 1

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Ngoc Anh Nguyen, Sorin Olaru, Pedro Rodriguez-Ayerbe, Morten Hovd, Necoara Ion. Fully inverse parametric linear/quadratic programming problems via convex liftings. Developments in Model-Based Optimization and Control , 464, pp.27-47, 2015. ⟨hal-01259951⟩

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