Exact conic programming reformulations of two-stage adjustable robust linear programs with new quadratic decision rules

Abstract

In this paper we introduce a new parameterized Quadratic Decision Rule (QDR), a generalisation of the commonly employed Affine Decision Rule (ADR), for two-stage linear adjustable robust optimization problems with ellipsoidal uncertainty and show that (affinely parameterized) linear adjustable robust optimization problems with QDRs are numerically tractable by presenting exact semi-definite program and second order cone program reformulations. Under these QDRs, we also establish that exact conic program reformulations also hold for two-stage linear ARO problems, containing also adjustable variables in their objective functions. We then show via numerical experiments on lot-sizing problems with uncertain demand that adjustable robust linear optimization problems with QDRs improve upon the ADRs in their performance both in the worst-case sense and after simulated realization of the uncertain demand relative to the true solution.

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Correspondence to V. Jeyakumar.

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Woolnough, D., Jeyakumar, V. & Li, G. Exact conic programming reformulations of two-stage adjustable robust linear programs with new quadratic decision rules. Optim Lett 15, 25–44 (2021). https://doi.org/10.1007/s11590-020-01595-y

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Keywords

  • Adjustable robust optimization
  • Semi-definite programs
  • Second order cone programs
  • Ellipsoidal uncertainty
  • Robust linear optimization