# 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 ...
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### 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 ...
• 605
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### 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 ...
• 51
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### 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 ...
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### 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 "...
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### 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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