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Author Espinoza, D.; Moreno, E.
Title A primal-dual aggregation algorithm for minimizing conditional value-at-risk in linear programs Type
Year (up) 2014 Publication Computational Optimization And Applications Abbreviated Journal Comput. Optim. Appl.
Volume 59 Issue 3 Pages 617-638
Keywords Conditional value at risk; Aggregation techniques; Approximation methods; Sample average approximation
Abstract Recent years have seen growing interest in coherent risk measures, especially in Conditional Value-at-Risk (). Since is a convex function, it is suitable as an objective for optimization problems when we desire to minimize risk. In the case that the underlying distribution has discrete support, this problem can be formulated as a linear programming (LP) problem. Over more general distributions, recent techniques, such as the sample average approximation method, allow to approximate the solution by solving a series of sampled problems, although the latter approach may require a large number of samples when the risk measures concentrate on the tail of the underlying distributions. In this paper we propose an automatic primal-dual aggregation scheme to exactly solve these special structured LPs with a very large number of scenarios. The algorithm aggregates scenarios and constraints in order to solve a smaller problem, which is automatically disaggregated using the information of its dual variables. We compare this algorithm with other common approaches found in related literature, such as an improved formulation of the full problem, cut-generation schemes and other problem-specific approaches available in commercial software. Extensive computational experiments are performed on portfolio and general LP instances.
Address [Espinoza, Daniel] Univ Chile, Dept Ind Engn, Santiago, Chile, Email: daespino@dii.uchile.cl;
Corporate Author Thesis
Publisher Springer Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0926-6003 ISBN Medium
Area Expedition Conference
Notes WOS:000344803000009 Approved
Call Number UAI @ eduardo.moreno @ Serial 424
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