# 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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### 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) ...
112 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 ...
298 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: (...
982 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.
660 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\\ &...
82 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?