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Fully Inverse Parametric Linear/Quadratic Programming Problems via Convex Liftings

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Developments in Model-Based Optimization and Control

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 464))

Abstract

In 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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Notes

  1. 1.

    Note that a slightly more involved definition of a cell complex exists in the literature [14, 28]. However, for simplicity, we mention only the property of interest in the present context.

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Acknowledgments

The first author would like to thank Dr. Martin Gulan, Dr. Michal Kvasnica, Prof. Miroslav Fikar, Dr. Sasa Rakovic, Prof. Franz Aurenhammer, and Prof. Boris Rohal’-Ilkiv for fruitful discussions and exchanges on topics related to this work.

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Authors and Affiliations

  1. Laboratory of Signals and Systems, CentraleSupélec-CNRS-Université Paris-Sud, Université Paris-Saclay, 3 Rue Joliot Curie, 91192, Paris, Gif-sur-Yvette, France

    Ngoc Anh Nguyen, Sorin Olaru & Pedro Rodriguez-Ayerbe

  2. Department of Engineering Cybernetics, Norwegian University of Science and Technology, 7491, Trondheim, Norway

    Morten Hovd

  3. Automatic Control and Systems Engineering Department, Politehnica University of Bucharest, Splaiul Independentei, 313, Bucharest, Romania

    Ion Necoara

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  1. Ngoc Anh Nguyen
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  2. Sorin Olaru
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  3. Pedro Rodriguez-Ayerbe
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  4. Morten Hovd
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  5. Ion Necoara
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Correspondence to Ngoc Anh Nguyen .

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Editors and Affiliations

  1. Laboratory of Signals and Systems, CentraleSupélec-CNRS-Université Paris-Sud, Université Paris-Saclay, Gif sur Yvette, France

    Sorin Olaru

  2. Department of Industrial Automation, Univ. of Chem.Tech. and Metallurgy Department of Industrial Automation, Sofia, Bulgaria

    Alexandra Grancharova

  3. Faculty of Engineering, Porto University Faculty of Engineering, Porto, Portugal

    Fernando Lobo Pereira

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Nguyen, N.A., Olaru, S., Rodriguez-Ayerbe, P., Hovd, M., Necoara, I. (2015). Fully Inverse Parametric Linear/Quadratic Programming Problems via Convex Liftings. In: Olaru, S., Grancharova, A., Lobo Pereira, F. (eds) Developments in Model-Based Optimization and Control. Lecture Notes in Control and Information Sciences, vol 464. Springer, Cham. https://doi.org/10.1007/978-3-319-26687-9_2

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  • DOI: https://doi.org/10.1007/978-3-319-26687-9_2

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