NDLI: The C3 Theorem and a D2 Algorithm for Large Scale Stochastic Mixed-Integer Programming: Set Convexification

Content Provider	Springer Nature Link
Author	Sen, Suvrajeet Higle, Julia L.
Copyright Year	2005
Abstract	This paper considers the two-stage stochastic integer programming problem, with an emphasis on instances in which integer variables appear in the second stage. Drawing heavily on the theory of disjunctive programming, we characterize convexifications of the second stage problem and develop a decomposition-based algorithm for the solution of such problems. In particular, we verify that problems with fixed recourse are characterized by scenario-dependent second stage convexifications that have a great deal in common. We refer to this characterization as the C3 (Common Cut Coefficients) Theorem. Based on the C3 Theorem, we develop a decomposition algorithm which we refer to as Disjunctive Decomposition (D2). In this new class of algorithms, we work with master and subproblems that result from convexifications of two coupled disjunctive programs. We show that when the second stage consists of 0-1 MILP problems, we can obtain accurate second stage objective function estimates after finitely many steps. This result implies the convergence of the D2 algorithm.
Starting Page	1
Ending Page	20
Page Count	20
File Format	PDF
ISSN	00255610
Journal	Mathematical Programming
Volume Number	104
Issue Number	1
e-ISSN	14364646
Language	English
Publisher	Springer-Verlag
Publisher Date	2005-04-28
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Stochastic Mixed-Integer Programming Disjunctive Programming Cutting Plane Algorithms Mathematics of Computing Numerical Analysis Combinatorics Calculus of Variations and Optimal Control Optimization Mathematical and Computational Physics Mathematical Methods in Physics Numerical and Computational Methods Operations Research/Decision Theory
Content Type	Text
Resource Type	Article
Subject	Mathematics Software

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