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Quadratic Two-Stage Stochastic Optimization with Coherent Measures of Risk

JIE SUN(JIE.SUN***at***CURTIN.EDU.AU)
LIZHI LIAO(LILIAO***at***HKBU.EDU.HK)
RODRIGUES BRIAN(BRIANR***at***SMU.EDU.SG)

Abstract: A new scheme to cope with two-stage stochastic optimization problems uses a risk measure as the objective function of the recourse action, where the risk measure is defined as the worst-case expected values over a set of constrained distributions. This paper develops an approach to deal with the case where both the first and second stage objective functions are convex linear-quadratic. It is shown that under a standard set of regularity assumptions, this two-stage quadratic stochastic optimization problem with measures of risk is equivalent to a conic optimization problem that can be solved in polynomial time.

Keywords: Conic duality quadratic programs risk measures stochastic optimization

Category 1: Stochastic Programming

Category 2: Robust Optimization

Category 3: Linear, Cone and Semidefinite Programming

Citation: Technical Report, Department of Mathematics and Statistics, Curtin University, Bentley, Australia, Feb. 2016

Download: [PDF]

Entry Submitted: 09/14/2016
Entry Accepted: 09/14/2016
Entry Last Modified: 09/14/2016

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