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SPEPS Preprint

Author(s): Suvrajeet Sen, University of Arizona
Julia L. Higle, University of Arizona
Title: The C 3 theorem and a D 2 algorithm for large scale stochastic integer programming – Set convexification
Date of Acceptance: 19.12.2000
Submission Date: 10.10.2000
Series Title: Stochastic Programming E-Print Series
(SPEPS)
Editors: Julie L. Higle; Werner Römisch; Surrajeet Sen
Keywords (eng): Stochastic Mixed-Integer Programming, Disjunctive Programming, Cutting Plane Algorithms
Appeared in: Mathematical programming 1 (Vol. 104, 2005)
Springer (Berlin [u.a.])
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Abstract (eng):
This paper considers the two stage stochastic integer programming problems, with an emphasis on problems 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 C^3 (Common Cut Coefficients) Theorem. Based on the C^3 Theorem, we develop an algorithmic methodology that we refer to as Disjunctive Decomposition (D^2). We show that when the second stage consists of 0-1 MILP problems , we can obtain accurate second stage objective function estimates afer finitely many steps. We also set the stage for comparisions between problems in which the first stage includes only 0-1 variables and those that allow both continuous and integer variables in the first stage.
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PDF 3 1   7 2 1 4 4 6 1 1 8 3 1 1 4 2 5 8 16 13 21 10 4 3 3 2 2 9 12 7

Gesamtzahl der Zugriffe seit Jul 2011:

  • Startseite – 55 (1.72 pro Monat)
  • PDF – 164 (5.13 pro Monat)
 
 
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