Regularized decomposition of high-dimensional multistage stochastic programs with Markov uncertainty

Tsvetan Asamov, Warren Buckler Powell

Research output: Contribution to journalArticle

7 Scopus citations

Abstract

We develop a quadratic regularization approach for the solution of high-dimensional multistage stochastic optimization problems characterized by a potentially large number of time periods/stages (e.g., hundreds), a high-dimensional resource state variable, and a Markov information process. The resulting algorithms are shown to converge to an optimal policy after a finite number of iterations under mild technical assumptions. Computational experiments are conducted using the setting of optimizing energy storage over a large transmission grid, which motivates both the spatial and temporal dimensions of our problem. Our numerical results indicate that the proposed methods exhibit significantly faster convergence than their classical counterparts, with greater gains observed for higher-dimensional problems.

Original languageEnglish (US)
Pages (from-to)575-595
Number of pages21
JournalSIAM Journal on Optimization
Volume28
Issue number1
DOIs
StatePublished - Jan 1 2018

All Science Journal Classification (ASJC) codes

  • Software
  • Theoretical Computer Science

Keywords

  • Multistage stochastic optimization
  • Nested decomposition
  • Quadratic regularization
  • Stochastic dual dynamic programming

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