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Multistage quadratic stochastic programming

Authors
Journal
Journal of Computational and Applied Mathematics
0377-0427
Publisher
Elsevier
Publication Date
Volume
129
Identifiers
DOI: 10.1016/s0377-0427(00)00545-8
Keywords
  • Piecewise Quadratic Function
  • Generalized Newton Method
  • Stochastic Programming
  • Multistage
Disciplines
  • Computer Science
  • Mathematics

Abstract

Abstract Quadratic stochastic programming (QSP) in which each subproblem is a convex piecewise quadratic program with stochastic data, is a natural extension of stochastic linear programming. This allows the use of quadratic or piecewise quadratic objective functions which are essential for controlling risk in financial and project planning. Two-stage QSP is a special case of extended linear-quadratic programming (ELQP). The recourse functions in QSP are piecewise quadratic convex and Lipschitz continuous. Moreover, they have Lipschitz gradients if each QP subproblem is strictly convex and differentiable. Using these properties, a generalized Newton algorithm exhibiting global and superlinear convergence has been proposed recently for the two stage case. We extend the generalized Newton algorithm to multistage QSP and show that it is globally and finitely convergent under suitable conditions. We present numerical results on randomly generated data and modified publicly available stochastic linear programming test sets. Efficiency schemes on different scenario tree structures are discussed. The large-scale deterministic equivalent of the multistage QSP is also generated and their accuracy compared.

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