Decomposition

ISE 5230 Decomposition Techniques in Mathematical Programming

This course provides a description of decomposition techniques to solve large-scale optimization problems with decomposable structure. Partitioning techniques considered include Dantzig-Wolfe, Benders and Lagrangian decompositions. The considered techniques are illustrated using examples and case studies from the energy sector.

Contents:

0. Welcome

Welcome to ISE 5230

0 DTMP

1. LP with complicating constraints

1 LPwithCC

1a LPwithCC_Examples

2. LP with complicating variables

2 LPwithCV

2a LPwithCV_Examples

3. NLP duality

3 NLPduality

3a NLPSensitivity

4. NLP with complicating constraints

4a NLPwithCC_1

4b NLPwithCC_2

4c NLPwithCC_3

4d NLPwithCC_Examples

4e fromLRtoDW

4f Multipliers

5. NLP with complicating variables

5 NLPwithCV

5a NLPwithCV_Examples

5b SensitivityBenders

6. Mixed-integer programming decomposition

6 MIPpartitioning

6a MIPpartitioning_Examples

7. Applications

Textbook:

A. J. Conejo, E. Castillo, R. Minguez, R. Garcia-Bertrand. Decomposition Techniques in Mathematical Programming. Engineering and Science Applications. Springer, Heidelberg. 2006