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On Solving Two-Stage Distributionally Robust Disjunctive Programs with a General Ambiguity Set

Manish Bansal (bansal***at***vt.edu)
Sanjay Mehrotra (mehrotra***at***northwestern.edu)

Abstract: We introduce two-stage distributionally robust disjunctive programs (TSDR-DPs) with disjunctive constraints in both stages and a general ambiguity set for the probability distributions. The TSDR-DPs subsume various classes of two-stage distributionally robust programs where the second stage problems are non-convex programs (such as mixed binary programs, semi-continuous program, general quadratic programs, separable non-linear programs, etc.). TSDR-DP is an optimization model with an adjustable level of risk-aversion. It generalizes: two-stage stochastic disjunctive program (risk-neutral) and two-stage robust disjunctive program (most-conservative). To our knowledge, these foregoing TSDR-DPs have not been studied up till now. In this paper, we develop decomposition algorithms, which utilize Balas' linear programming equivalent for deterministic disjunctive programs or his sequential convexification approach within L-shaped method, to solve TSS-DPs. We present sufficient conditions under which our algorithms are finitely convergent. These algorithms generalize the distributionally robust integer L-shaped algorithm of Bansal et al. (SIAM J. on Optimization, 2018) for TSDR mixed binary programs, a subclass of TSDR-DPs. Furthermore, we formulate a semi-continuous program (SCP) as a disjunctive program and use our results for TSDR-DPs to solve general two-stage distributionally robust SCPs (TSDR-SCPs) and TSDR-SCP having semi-continuous inflow set in the second stage.

Keywords: Stochastic Programming; Distributionally robust disjunctive programs; decomposition algorithms; sequential convexification; parametric cutting planes

Category 1: Stochastic Programming

Category 2: Integer Programming (0-1 Programming )

Citation: Technical Report#B1811, Virginia Tech, August 2018.

Download: [PDF]

Entry Submitted: 08/07/2018
Entry Accepted: 08/08/2018
Entry Last Modified: 02/11/2019

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