Journal of Optimization Theory and Applications

, Volume 158, Issue 2, pp 576–589

A Polynomial-Time Solution Scheme for Quadratic Stochastic Programs

Article

DOI: 10.1007/s10957-012-0264-6

Cite this article as:
Rocha, P. & Kuhn, D. J Optim Theory Appl (2013) 158: 576. doi:10.1007/s10957-012-0264-6
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Abstract

We consider quadratic stochastic programs with random recourse—a class of problems which is perceived to be computationally demanding. Instead of using mainstream scenario tree-based techniques, we reduce computational complexity by restricting the space of recourse decisions to those linear and quadratic in the observations, thereby obtaining an upper bound on the original problem. To estimate the loss of accuracy of this approach, we further derive a lower bound by dualizing the original problem and solving it in linear and quadratic recourse decisions. By employing robust optimization techniques, we show that both bounding problems may be approximated by tractable conic programs.

Keywords

Decision rule approximation Robust optimization Quadratic stochastic programming Conic programming 

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of ComputingImperial College LondonLondonUK