# 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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### Totally unimodular towards linear programming relaxation

I'm currently studying about totally unimodular. I was reading this link: https://ostad.nit.ac.ir/upload/Integer_Programming_1.pdf, from page 38-41 and I came across the statement: 'It is clear that ...
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### How to transform this BIP into LP with the help of penalty function?

I have an BIP problem as below $$\underset{\bf b}{\max}{\bf u}^T\bf b$$ $$\text{subject to}$$ $${\bf Ab}\le1$$ Here, ${\bf b}=\{b_1,b_2,\cdots,b_N\}$ is a column vector of decision/optimization ...
479 views

### I ran a relaxed MIP and got some integer results; how can I constrain MIP to match those integers?

Suppose I run a relaxation of an MIP. If my result is all integers, I have achieved the same min/max that the MIP would achieve. However, what can I say if some portion of my result is integer? If ...
186 views

### KKT conditions analysis for binary constraints

I am wondering if boolean constraints in a linear program can be solved (after linear relaxation from $x\in\{0,1\}$ to both $x\ge0$ and $x\le1$) using KKT analysis. Most of the algorithms that I have ...
175 views

### Linear Relaxation of Boolean Constraint for Solving Integer Linear Program Using KKT

I am trying to convert a boolean LP to LP using LP relaxation by converting $x \in {0,1}$ to both $x \ge 0$ and $x \le 1$. Then to use it in my problem analysis, I am trying to build the KKT ...
143 views

### Is there any academic reference which suggests/uses dual values as initialization of Lagrangian multipliers?

The Lagrangian relaxation approach is used to generate lower (upper) bounds for minimization (maximization) problems by moving some constraints to the objective function and multiplying them by "...
143 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 ...
256 views

### Obtaining linear relaxation objective value from MILP model coded in Pyomo

I would like to seek some advice on modeling the following: I am currently using Pyomo to generate my MILP model in Pyomo. It seems that it is not possible to cast the integer and binary variables to ...
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### 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 ...
238 views