Learning algorithms for separable approximations of discrete stochastic optimization problems

Learning algorithms for separable approximations of discrete stochastic optimization problems

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Article ID: iaor20072599
Country: United States
Volume: 29
Issue: 4
Start Page Number: 814
End Page Number: 836
Publication Date: Nov 2004
Journal: Mathematics of Operations Research
Authors: , ,
Abstract:

We propose the use of sequences of separable, piecewise linear approximations for solving nondifferentiable stochastic optimization problems. The approximations are constructed adaptively using a combination of stochastic subgradient information and possibly sample information on the objective function itself. We prove the convergence of several versions of such methods when the objective function is separable and has integer break points, and we illustrate their behavior on numerical examples. We then demonstrate the performance on nonseparable problems that arise in the context of two-stage stochastic programming problems, and demonstrate that these techniques provide near-optimal solutions with a very fast rate of convergence compared with other solution techniques.

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