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Characterizations of Robust and Stable Duality for Linearly Perturbed Uncertain Optimization Problems

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From Analysis to Visualization (JBCC 2017)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 313))

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Abstract

We introduce a robust optimization model consisting in a family of perturbation functions giving rise to certain pairs of dual optimization problems in which the dual variable depends on the uncertainty parameter. The interest of our approach is illustrated by some examples, including uncertain conic optimization and infinite optimization via discretization. The main results characterize desirable robust duality relations (as robust zero-duality gap) by formulas involving the epsilon-minima or the epsilon-subdifferentials of the objective function. The two extreme cases, namely, the usual perturbational duality (without uncertainty), and the duality for the supremum of functions (duality parameter vanishing) are analyzed in detail.

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Acknowledgements

This research was supported by the Vietnam National University - HCM city, Vietnam, project B2019-28-02, by PGC2018-097960-B-C22 of the Ministerio de Ciencia, Innovación y Universidades (MCIU), the Agencia Estatal de Investigación (AEI), and the European Regional Development Fund (ERDF), and by the Australian Research Council, Project DP180100602.

Author information

Authors and Affiliations

  1. International University, Vietnam National University - HCMC, Linh Trung ward, Ho Chi Minh city, Thu Duc district, Vietnam

    Nguyen Dinh

  2. Department of Mathematics, University of Alicante, Alicante, Spain

    Miguel A. Goberna & Marco A. López

  3. CIAO, Federation University, Ballarat, Australia

    Marco A. López

  4. LMA, Avignon University, EA 2151, Avignon, France

    Michel Volle

Authors
  1. Nguyen Dinh
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  2. Miguel A. Goberna
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  3. Marco A. López
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  4. Michel Volle
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Corresponding author

Correspondence to Miguel A. Goberna .

Editor information

Editors and Affiliations

  1. Lawrence Berkeley National Laboratory, Berkeley, CA, USA

    David H. Bailey

  2. Western University, London, ON, Canada

    Naomi Simone Borwein

  3. Mathematical Sciences Institute, Australian National University, Canberra, ACT, Australia

    Richard P. Brent

  4. School of IT and Mathematical Sciences, University of South Australia, Mawson Lakes, SA, Australia

    Regina S. Burachik

  5. School of Mathematical and Physical Sciences, University of Newcastle, Callaghan, NSW, Australia

    Judy-anne Heather Osborn

  6. School of Mathematical and Physical Sciences, University of Newcastle, Callaghan, NSW, Australia

    Brailey Sims

  7. Department of Mathematics, Western Michigan University, Kalamazoo, MI, USA

    Qiji J. Zhu

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Dinh, N., Goberna, M.A., López, M.A., Volle, M. (2020). Characterizations of Robust and Stable Duality for Linearly Perturbed Uncertain Optimization Problems. In: Bailey, D., et al. From Analysis to Visualization. JBCC 2017. Springer Proceedings in Mathematics & Statistics, vol 313. Springer, Cham. https://doi.org/10.1007/978-3-030-36568-4_4

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