25
votes
Accepted
What's the difference between Lagrangian relaxation and Lagrangian decomposition?
They are not the same thing. Lagrangian decomposition is a special case of Lagrangian relaxation.
(Note: I'm talking specifically about integer programming problems in this answer, though some of ...
- 13.2k
14
votes
What are the modern optimization methods for large systems?
The gap between industry and academia is huge.
My suggestion for a future professional would be to learn very good coding because without that skill people are very limited.
What I have seen in ...
- 12.2k
8
votes
Textbook recommendation for linear programming decomposition fundamentals
I propose reading the following textbook:
Linear Programming and Network Flows by by Hanif D. Sherali, John J.
Jarvis, and M. S. Bazaraa
I read the first 7 chapters of the book a long time ago (...
- 2,170
7
votes
Textbook recommendation for linear programming decomposition fundamentals
I took the course 42136 for Benders decomposition and Dantzig-Wolfe (DW) decomposition at Technical University of Denmark. Besides the textbook [conejo2006decomposition] (mentioned by @A.Omidi as well)...
- 391
4
votes
Decomposition methods for two-stage stochastic program with integer variables
To solve stochastic programming models with integer recourse, there are some methods. Most stochastic programming textbooks cover these methods. For example, chapter 7 of Introduction to Stochastic ...
- 2,473
4
votes
What are the modern optimization methods for large systems?
It is also my impression that decomposition methods are not widely used in a commercial context. In the industry, you often make an "effort vs. value" estimation to decide what methods to use. This ...
- 1,659
4
votes
The variable splitting scheme in the context of Lagrangian relaxation
I am familiar with variable splitting (also known as Lagrangian decomposition) being applied to facility location problems. We used it in our paper:
Snyder and Daskin, Stochastic $p$-robust location ...
- 13.2k
4
votes
The variable splitting scheme in the context of Lagrangian relaxation
The only occurrences of this decomposition that I am aware of are from:
Jörnsten K, Näsberg M (1986) A new Lagrangian relaxation approach to the generalized assignment problem. European Journal of ...
- 2,673
4
votes
Textbook recommendation for linear programming decomposition fundamentals
Some more references, different than those in the other answers. I added some application papers too. I often find a practical example rather helpful to understand a specific technique.
Classical ...
- 3,481
3
votes
multi stage stochastic programming algorithm
If your question is “Are nested Benders decomposition or progressive hedging more efficient than solving a very large-scale monolithic formulation (sometimes called ‘deterministic equivalent’) with ...
- 136
2
votes
Accepted
Decomposition methods for two-stage stochastic program with integer variables
You can try a master problem of the form
\begin{alignat*}{1}
\min & \quad \gamma\\
\textrm{s.t.} & \quad \sum_{s=1}^{S}P_{s}Y_{s}\le\alpha\\
& \quad \gamma\ge\gamma_{T}\left[\sum_{s\in T}(...
- 40.1k
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