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Exact conic programming reformulations of two-stage adjustable robust linear programs with new quadratic decision rules
Optimization Letters ( IF 1.3 ) Pub Date : 2020-05-25 , DOI: 10.1007/s11590-020-01595-y
D. Woolnough , V. Jeyakumar , G. Li

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.



中文翻译:

具有新的二次决策规则的两阶段可调鲁棒线性程序的精确圆锥编程公式

在本文中,我们介绍了一种新的参数化二次决策规则(QDR),它是常用的仿射决策规则(ADR)的推广,用于具有椭圆形不确定性的两阶段线性可调鲁棒优化问题,并证明了(仿射参数化)线性可调鲁棒通过提供精确的半定程序和二阶锥程序重新公式化,可以轻松解决QDR的优化问题。在这些QDR下,我们还确定了精确的圆锥程序重新公式化也适用于两阶段线性ARO问题,其目标函数中还包含可调整的变量。

更新日期:2020-05-25
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