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 ...
LarrySnyder610's user avatar
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 ...
Nikos Kazazakis's user avatar
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 (...
rasul's user avatar
  • 2,140
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)...
Edward's user avatar
  • 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 ...
Ehsan's user avatar
  • 2,463
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 ...
Michael Lindahl's user avatar
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 ...
LarrySnyder610's user avatar
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 ...
fontanf's user avatar
  • 2,623
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 ...
Joris Kinable's user avatar
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 ...
Tim Varelmann's user avatar
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}(...
prubin's user avatar
  • 39.1k

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