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Mathematics > Optimization and Control

arXiv:1812.09879 (math)
[Submitted on 24 Dec 2018]

Title:On Risk-Averse Stochastic Semidefinite Programs with Continuous Recourse

Authors:Matthias Claus, Rüdiger Schultz, Kai Spürkel, Tobias Wollenberg
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Abstract:The vast majority of the literature on stochastic semidefinite programs (stochastic SDPs) with recourse is concerned with risk-neutral models. In this paper, we introduce mean-risk models for stochastic SDPs and study structural properties as convexity and (Lipschitz) continuity. Special emphasis is placed on stability with respect to changes of the underlying probability distribution. Perturbations of the true distribution may arise from incomplete information or working with (finite discrete) approximations for the sake of computational efficiency. We discuss extended formulations for stochastic SDPs under finite discrete distributions, which turn out to be deterministic (mixed-integer) SDPs that are (almost) block-structured for many popular risk measures.
Subjects: Optimization and Control (math.OC)
MSC classes: 90C15, 90C31
Cite as: arXiv:1812.09879 [math.OC]
  (or arXiv:1812.09879v1 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.1812.09879

Submission history

From: Matthias Claus [view email]
[v1] Mon, 24 Dec 2018 10:19:43 UTC (39 KB)
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