Two-stage stochastic programming with linearly bi-parameterized quadratic recourse

JUNYI LIU, YING CUI, JONG SHI PANG, SUVRAJEET SEN

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6 Scopus citations

Abstract

This paper studies the class of two-stage stochastic programs with a linearly biparameterized recourse function defined by a convex quadratic program. A distinguishing feature of this new class of nonconvex stochastic programs is that the objective function in the second stage is linearly parameterized by the first-stage decision variable, in addition to the standard linear parameterization in the constraints. While a recent result has established that the resulting recourse function is of the difference-of-convex (dc) kind, the associated dc decomposition of the recourse function does not provide an easy way to compute a directional stationary solution of the two-stage stochastic program. Based on an implicit convex-concave property of the bi-parameterized recourse function, we introduce the concept of a generalized critical point of such a recourse function and provide a sufficient condition for such a point to be a directional stationary point of the stochastic program. We describe an iterative algorithm that combines regularization, convexification, and sampling and establish the subsequential convergence of the algorithm to a generalized critical point, with probability.

Original languageEnglish (US)
Pages (from-to)2530-2558
Number of pages29
JournalSIAM Journal on Optimization
Volume30
Issue number3
DOIs
StatePublished - 2020

Bibliographical note

Publisher Copyright:
© 2020 Society for Industrial and Applied Mathematics.

Keywords

  • Difference-of-convex
  • Directional stationarity
  • Two-stage stochastic programming

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