T he purpose of this paper is to introduce a new test-problem collection for stochastic linear programming that the authors have recently begun to assemble. While there are existing stochastic programming test-problem collections, our new collection has three features that distinguish it from existing collections. First, our collection is web-based with free public access, and we intend to enrich it as new test problems become available. Indeed, we encourage submissions of new test problems. Second, along with the collection we provide documentation of the problems, so that researchers can quickly find information about each family without reading through the original source. Third, all of the data in our collection are provided in SMPS (Birge et al. 1987, Gassmann andSchweitzer 2001) format. In this paper, we provide an introduction to the stochastic linear program, give a brief description of each problem family currently in the test-problem collection, and describe the documentation that accompanies the collection.
Semidefinite programs are a class of optimization problems that have been studied extensively during the past 15 years. Semidefinite programs are naturally related to linear programs, and both are defined using deterministic data. Stochastic programs were introduced in the 1950s as a paradigm for dealing with uncertainty in data defining linear programs. In this paper, we introduce stochastic semidefinite programs as a paradigm for dealing with uncertainty in data defining semidefinite programs.Keywords Linear programming · Stochastic programming · Recourse · Semidefinite programming MSC Classification 90C15 · 90C51 · 90C05
Abstract. Ariyawansa and Zhu have recently proposed a new class of optimization problems termed stochastic semidefinite 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 andÖzevin 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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