Quadratic two-stage stochastic optimization with coherent measures of risk

• Main Authors: SUN, Jie, LIAO, Li-Zhi, RODRIGUES, Brian
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2018
• Subjects: Conic duality; Quadratic programs; Risk measures; Stochastic optimization; Operations and Supply Chain Management; Operations Research, Systems Engineering and Industrial Engineering
• Online Access: https://ink.library.smu.edu.sg/lkcsb_research/5155; https://ink.library.smu.edu.sg/context/lkcsb_research/article/6154/viewcontent/QuadraticTwo_stageStochasticOptimizationCoherent_2017_afv.pdf
• Institution: Singapore Management University

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.