# Questions tagged [lp-relaxation]

For questions relating to the relaxation of linear integer or mixed-integer-linear programming (MILP) problems where the integer constraints are removed.

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### What is a general procedure to prove that the LP relaxation of an IP delivers the optimal IP solution?

Say that I have a binary IP $$z=\max_x \{c^\top x: Ax=b, x\in B^n\}$$ where $B^n$ is the set of $n$-dimensional $0-1$ vectors. Its LP relaxation will be z^{LP}=\max_x \{c^\top x: Ax=b, 0\leq x\leq 1\...
87 views

### What is the difference between root relaxation and LP relaxation

(I apologize. I saw this question but, I do not know these may be the same or not.) I am trying to solve a MIP problem and have an issue about that. The problem's LP relaxation has the objective ...
62 views

### Problem related to machine's performance while solving an LP-relaxation of a set-covering problem using the Column Generation

PS: I am familiar with performance variability encountered while solving large-scale MIPs. My question may not be explicitly related to it but maybe to the inefficiency of python packages. I have ...
227 views

### Cplex 12.10: How can I solve an LP relaxation?

I have an IloCplex object which contains a MILP. Is there a way to obtain the objective value of its LP relaxation, without having to rewrite the entire model as ...
69 views

### What to do with cuts (constraints) when a fixation is contrary to a RHS in a ILP / LP relaxation?

I am trying to understand an algorithm in a paper by Crévits et al. (2012)1 (see algorithm 2, the cuts I'm referring to are from the reduced costs). It uses a series of successive cuts on a linear ...
930 views

### Is This Constraint Convex?

I have a constraint that I believe to be convex and not affine which I think means that I can implement a relaxation. I will first define the full constraint, and then build up my (informal) reasoning ...
1k views

### How to compare two different formulations of a problem?

I somewhat know how to compare two MILP formulations of a problem that both use the same set of decision variables (as in the classical MTZ vs DFJ formulations of the TSP). I was wondering how two ...
### Symmetric undirected $p$-median instance with fractional LP solution?
The $p$-median problem is NP-hard, so its LP relaxation does not naturally have all-integer solutions. However, it very often does; in fact, it can be hard to find an instance for which the LP ...