# Tag Info

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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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