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Generalized Decision Rule Approximations for Stochastic Programming via Liftings

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  • Angelos Georghiou
  • Wolfram Wiesemann
  • Daniel Kuhn

Abstract

Stochastic programming provides a versatile framework for decision-making under uncertainty, but the resulting optimization problems can be computationally demanding. It has recently been shown that, primal and dual linear decision rule approximations can yield tractable upper and lower bounds on the optimal value of a stochastic program. Unfortunately, linear decision rules often provide crude approximations that result in loose bounds. To address this problem, we propose a lifting technique that maps a given stochastic program to an equivalent problem on a higherdimensional probability space. We prove that solving the lifted problem in primal and dual linear decision rules provides tighter bounds than those obtained from applying linear decision rules to the original problem. We also show that there is a one-to-one correspondence between linear decision rules in the lifted problem and families of non-linear decision rules in the original problem. Finally, we identify structured liftings that give rise to highly flexible piecewise linear decision rules and assess their performance in the context of a stylized investment planning problem.

Suggested Citation

  • Angelos Georghiou & Wolfram Wiesemann & Daniel Kuhn, 2010. "Generalized Decision Rule Approximations for Stochastic Programming via Liftings," Working Papers 043, COMISEF.
  • Handle: RePEc:com:wpaper:043
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    File URL: http://comisef.eu/files/wps043.pdf
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    1. repec:spr:joptap:v:171:y:2016:i:3:d:10.1007_s10957-016-0920-3 is not listed on IDEAS
    2. Rocha, Paula & Kuhn, Daniel, 2012. "Multistage stochastic portfolio optimisation in deregulated electricity markets using linear decision rules," European Journal of Operational Research, Elsevier, vol. 216(2), pages 397-408.

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