Stochastic Programming Approach to Optimization under Uncertainty

Alexander Shapiro (ashapiroisye.gatech.edu)

Abstract: In this paper we discuss computational complexity and risk averse approaches to two and multistage stochastic programming problems. We argue that two stage (say linear) stochastic programming problems can be solved with a reasonable accuracy by Monte Carlo sampling techniques while there are indications that complexity of multistage programs grows fast with increase of the number of stages. We discuss an extension of coherent risk measures to a multistage setting and, in particular, dynamic programming equations for such problems.

Keywords: two and multistage stochastic programming, complexity, Monte Carlo sampling, sample average approximation method, coherent risk measures, dynamic programming, conditional risk mappings.

Category 1: Stochastic Programming

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Entry Submitted: 01/31/2006
Entry Accepted: 01/31/2006
Entry Last Modified: 06/06/2006

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