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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 this answer applies to continuous optimization as well.) Lagrangian relaxation involves removing (relaxing) one or more constraints and penalizing violations of ...


8

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 (during my Bachelor studies), and I really enjoyed it. Chapter 7 of the book titled THE DECOMPOSITION PRINCIPLE introduces Dantzig-Wolfe decomposition and its ...


7

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), following materials are recommended: [carøe1998l], chapter 5.1 in [birge2011introduction] for L-shaped Benders Decomposition, in terms of two-stage (...


6

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 practice is that it's impossible to gauge how useful an algorithm/method is without trying it out first, so the most important skill is the skill to do try ...


4

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 Programming by Birge and Louveux covers these techniques. In particular, I suggest either using the integer L-shaped method or the progressive hedging algorithm (...


4

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 will often not favor decomposition algorithms due to a relatively high effort and the risk of it not providing better results. I would make the following ...


4

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 Benders decompositon: Martin R.K. (1999) Projection: Benders’ Decomposition. In: Large Scale Linear and Integer Optimization: A Unified Approach. Springer, Boston, ...


2

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}(1-Y_{s})-|T|+1\right]\quad\forall T\in\mathcal{T}\\ & \quad Y_{s}\in\left\{ 0,1\right\} \quad\forall s\in\left\{ 1,\dots,S\right\} \end{alignat*} where $\...


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