Stochastic second-order cone programming: Applications models

Second-order cone programs are a class of convex optimization problems. We refer to them as deterministic second-order cone programs (DSCOPs) since data defining them are deterministic. In DSOCPs we minimize a linear objective function over the intersection of an affine set and a product of second-o...

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Bibliographic Details
Published in:Applied mathematical modelling 2012-10, Vol.36 (10), p.5122-5134
Main Author: Alzalg, Baha M.
Format: Article
Language:English
Subjects:
Conic programming
Mathematical analysis
Mathematical models
Optimization
Optimization models
Programming
Second-order cone programming
Stochastic programming
Stochasticity
Uncertainty
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Summary:Second-order cone programs are a class of convex optimization problems. We refer to them as deterministic second-order cone programs (DSCOPs) since data defining them are deterministic. In DSOCPs we minimize a linear objective function over the intersection of an affine set and a product of second-order (Lorentz) cones. Stochastic programs have been studied since 1950s as a tool for handling uncertainty in data defining classes of optimization problems such as linear and quadratic programs. Stochastic second-order cone programs (SSOCPs) with recourse is a class of optimization problems that defined to handle uncertainty in data defining DSOCPs. In this paper we describe four application models leading to SSOCPs.
ISSN:0307-904X
DOI:10.1016/j.apm.2011.12.053