A Scenario Decomposition Algorithm for Stochastic Programming Problems with a Class of Downside Risk Measures

• DOI: 10.1287/ijoc.2014.0635
• Publication Date: 2015-05-12T17:38:53Z
• Authors: Maciej Rysz; Alexander Vinel; Pavlo Krokhmal; Eduardo L. Pasiliao
• Keywords: Downside risk; Coherent risk measure

We present an efficient scenario decomposition algorithm for solving large-scale convex stochastic programming problems that involve a particular class of downside risk measures. The considered functionals encompass coherent and measures can be represented as infimal convolution certainty equivalent, include well-known measures, such conditional value-at-risk, special cases. resulting structure the feasible set is then exploited via iterative relaxed problems, it shown number iterations bounded by parameter depends on problem size. computational performance developed method illustrated portfolio optimization involving two families nonlinear risk, higher-moment log-exponential It demonstrated proposed approach provide up to order-of-magnitude improvement in time comparison state-of-the-art solvers, CPLEX, Gurobi, MOSEK.