stochastic semidefinite programming (SSDP) is a new class of optimization problems with a wide variety of applications. In this article, asymptotic analysis results of sample average approximation estimator for SSDP a...
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stochastic semidefinite programming (SSDP) is a new class of optimization problems with a wide variety of applications. In this article, asymptotic analysis results of sample average approximation estimator for SSDP are established. Asymptotic analysis result already existing for stochastic nonlinear programming is extended to SSDP, that is, the conditions ensuring the convergence in distribution of sample average approximation estimator for SSDP to a multivariate normal are obtained and the corresponding covariance matrix is described in a closed form. (C) 2020 Elsevier B.V. All rights reserved.
Ariyawansa and Zhu have proposed a new class of optimization problems termed stochasticsemidefinite programs to handle data uncertainty in applications leading to (deterministic) semidefinite programs. For stochastic...
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Ariyawansa and Zhu have proposed a new class of optimization problems termed stochasticsemidefinite programs to handle data uncertainty in applications leading to (deterministic) semidefinite programs. For stochasticsemidefinite programs with finite event space, they have also derived a class of volumetric barrier decomposition algorithms, and proved polynomial complexity of certain members of the class. In this paper, we consider homogeneous self-dual algorithms for stochasticsemidefinite programs with finite event space. We show how the structure in such problems may be exploited so that the algorithms developed in this paper have complexity similar to those of the decomposition algorithms mentioned above.
The vast majority of the literature on stochasticsemidefinite programs (stochastic SDPs) with recourse is concerned with risk-neutral models. In this paper, we introduce mean-risk models for stochastic SDPs and study...
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The vast majority of the literature on stochasticsemidefinite 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.
Ariyawansa and Zhu have recently proposed a new class of optimization problems termed stochasticsemidefinite programs (SSDPs). SSDPs may be viewed as an extension of two-stage stochastic (linear) programs with recour...
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Ariyawansa and Zhu have recently proposed a new class of optimization problems termed stochasticsemidefinite programs (SSDPs). SSDPs may be viewed as an extension of two-stage stochastic (linear) programs with recourse (SLPs). Zhao has derived a decomposition algorithm for SLPs based on a logarithmic barrier and proved its polynomial complexity. Mehrotra and Ozevin have extended the work of Zhao to the case of SSDPs to derive a polynomial logarithmic barrier decomposition algorithm for SSDPs. An alternative to the logarithmic barrier is the volumetric barrier of Vaidya. There is no work based on the volumetric barrier analogous to that of Zhao for SLPs or to the work of Mehrotra and Ozevin for SSDPs. The purpose of this paper is to derive a class of volumetric barrier decomposition algorithms for SSDPs, and to prove polynomial complexity of certain members of the class.
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