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Worst-case-expectation approach to optimization under uncertainty

Alexander Shapiro(ashapiro***at***isye.gatech.edu)
Wajdi Tekaya(wtekaya***at***gatech.edu)
Murilo Pereira Soares(murilo***at***ons.org.br)
Joari Paulo da Costa(joari***at***ons.org.br)

Abstract: In this paper we discuss multistage programming with the data process subject to uncertainty. We consider a situation were the data process can be naturally separated into two components, one can be modeled as a random process, with a specified probability distribution, and the other one can be treated from a robust (worst case) point of view. We formulate this in a time consistent way and derive the corresponding dynamic programming equations. In order to solve the obtained multistage problem we develop a variant of the Stochastic Dual Dynamic Programming (SDDP) method. We give a general description of the algorithm and present computational studies related to planning of the Brazilian interconnected power system.

Keywords: Multistage stochastic programming, robust optimization, robust distribution stochastic programming, time consistency, dynamic equations, Stochastic Dual Dynamic Programming, sample average approximation, risk neutral and risk averse approaches, case studies

Category 1: Stochastic Programming

Category 2: Robust Optimization

Category 3: Applications -- OR and Management Sciences


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Entry Submitted: 10/30/2012
Entry Accepted: 10/31/2012
Entry Last Modified: 10/30/2012

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