Questions tagged [lagrangian-decomposition]

For questions related to Lagrangian decomposition, an optimization method in which one or more decision variable is doubled, the new variable is set equal to the original variable via a constraint, and that constraint is relaxed using Lagrangian relaxation.

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6 votes
0 answers
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Benders decomposition for a dense MILP

I am trying to solve a large MILP, but it seems like dense problems can be very difficult for moderns solvers. I tried to solve the problem described below considering only constraints (1) and (2) ...
2 votes
1 answer
67 views

multi stage stochastic programming algorithm

I have a multi-stage stochastic programming model. I have 3 groups of variables: the first group takes values at the beginning of the planning horizon before the first realization and does not change ...
  • 21
4 votes
2 answers
238 views

The variable splitting scheme in the context of Lagrangian relaxation

I am interested to know solving the generalized assignment problem (GAP) using the variable splitting scheme, specifically, in the context of Lagrangian relaxation. The problem is stated as follows: (...
  • 6,206
7 votes
3 answers
757 views

Textbook recommendation for linear programming decomposition fundamentals

I am looking for a textbook on linear programming decomposition fundamentals. The book should be clear and easy-to-follow for self study and should include examples to illustrate the concepts.
3 votes
2 answers
363 views

Decomposition methods for two-stage stochastic program with integer variables

In a stochastic programming problem, I have binary variables in the second stage. As an example, consider that the optimization problem is given by: \begin{align} &\text{minimize} &\gamma\\ &...
  • 151
2 votes
0 answers
78 views

Can every convex problem use Lagrangian dual method?

If not all constraints satisfy equalities, does Lagrangian dual method make sense to a convex problem?
15 votes
2 answers
472 views

What are the modern optimization methods for large systems?

I came across the preface of Optimization Theory for Large Systems (you can read it in Amazon). The author claims in the table (page v) that some of the methods such as Dantzig Wolfe decomposition, ...
  • 2,859
20 votes
1 answer
1k views

What's the difference between Lagrangian relaxation and Lagrangian decomposition?

What is the difference between Lagrangian relaxation and Lagrangian decomposition? Are they the same thing?