1 / 39

Decomposition Methods

Explore Constraint Matrix Block Systems, Benders Decomposition, Dantzig-Wolfe Decomposition, and their comparison. Learn about Two-Stage SLP, Primal Block Angular Structures, and wrap-up with conclusions on solving problems using decomposition methods. Understand how discrete and continuous SLP problems can be tackled efficiently through Benders or Dantzig-Wolfe methods.

kingmark
Download Presentation

Decomposition Methods

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Decomposition Methods Lecture 6 Leonidas Sakalauskas Institute of Mathematics and Informatics Vilnius, Lithuania EURO Working Group on Continuous Optimization

  2. Content • Constraint matrix block systems • Benders decomposition • Master problem and cuts • Dantzig-Wolfe decomposition • Comparison of Benders and Dantzig-Wolfe decompositions

  3. Two-stage SLP The two-stage stochastic linear programming problem can be stated as

  4. Two-Stage SLP Assume the set of scenarios K be finite and defibed by probabilities In continuous stochastic programming by the Monte-Carlo Method this is equivalent to

  5. Two-Stage SLP Using the definition of discrete random variable the SLP considered is equivalent to large linear problem with block constraint matrix:

  6. Block Diagonal

  7. Staircase Systems

  8. Block Angular

  9. Benders Decomposition

  10. Feasibility

  11. Dantzif-Wolfe Decomposition Primal Block Angular Structure

  12. The Problem

  13. Wrap-Up and conclusions • The discrete SLP is reduced to equivalent linear program with block constraint matrix, that solved by Benders or Dantzig-Wolfe decomposition method • The continuous SLP is solved by decomposition method simulating the finite set of random scenarios

More Related