# Questions tagged [linear-programming]

For questions related to problems that optimize (i.e., minimize or maximize) a linear objective subject to linear constraints.

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### In an integer program, how I can force a binary variable to equal 1 if some condition holds?

Suppose we have a binary or continuous variable $x$, a binary variable $y$, and a constant $b$, and we want to enforce a relationship like If $x \gtreqless b$, then $y = 1$. How can we write this ...
5k views

### How to linearize the product of two binary variables?

Suppose we have two binary variables $x$ and $y$. How can we linearize the product $xy$?
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### What are good reference books for introduction to operations research?

The reference books should cover the wide range of problem-solving techniques and methods.
4k views

### How to linearize the product of a binary and a non-negative continuous variable?

Suppose we have a binary variable $x$ and a non-negative continuous variable $y$. How can we linearize the product $x y$?
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### Why is it important to choose big-M carefully and what are the consequences of doing it badly?

The question here discusses the two different use of "big-M method", where one of them is the big-M in logical constraints and linearization in (mixed-)integer programming problems (that's what I'm ...
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### Optimization Problem Libraries

Can someone please make a list of optimization problem libraries so that the community can add to and refine it? I know a few off the top of my head.
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### How does a warm start work in LP/MIP?

Can someone explain how warm starts/ MIP starts work? How do solvers like CPLEX/GUROBI use warm start with the Simplex algorithm? I am interested in understanding how the entire warm start ...
409 views

### Linear and Integer programming materials

I was wondering if you could refer me to some online video/text resources to learn linear and integer programming. I am intending to work in the field of data science. I greatly appreciate your kind ...
974 views

### Where can I find open source LP solvers?

I'm familiar with COIN-OR and have also used a couple packages in R to solve LPs. Today I found out Google has their own open source optimization software, and it got me wondering what other open ...
1k views

### State-of-the-art algorithms for solving linear programs

Průša and Werner (2019) show that the general linear programming problem reduces in nearly linear time to the LP relaxations of many classical NP-hard problems (assuming sparse encoding of instances)....
3k views

### Linear Programming with additional “if-then”/“Default to zero” constraints?

What approaches can I use for a Linear Programming problem with the additional constraint that if a decision variable falls below a certain threshold, then it should just be forced to 0. I'm ...
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### How to linearize the product of two continuous variables?

Suppose we have two variables $x, y \in \mathbb R$. How can we linearize the product $xy$? If this cannot be done exactly, is there a way to get an approximate result?
395 views

### How to linearize a constraint with a maximum or minimum in the right-hand-side?

Suppose we have three variables, $x, y, z \in \mathbb R$. How can we linearize constraints with the following structure? $$z \geq \min(x, y)$$ $$z \leq \max(x, y)$$
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### Linearize or approximate a square root constraint

I encounter a nonlinear constraint that contains the square root of a sum of integer variables. Of course one could use nonlinear solvers and techniques; but I like linear programming. Are there any ...
2k views

### Find feasible point in polynomial time in linear programming

Background A while ago my team was implementing an interior point LP solver and we came across the following conundrum: Is there a polynomial-time algorithm to find a feasible starting point in ...
594 views

### Feeding known lower bounds to solvers

Given an optimization problem that aims at minimizing some objective function, a lower bound that is valid for all optimal solutions, and your solver of choice: For what theoretical and/or practical (...
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### How to evaluate the performance of open source solver?

I am looking for a reliable open source solver to solve LP and MILP (with a few thousand variables). How can I evaluate the performance of a given solver for a particular use case?
663 views

### Linear optimization problem with user-defined cost function

I have a linear optimization problem for which I am looking for a suitable optimization solution that can fulfill my requirements. Here is an explanation of the optimization problem: There are a ...
482 views

### Working with absolute values in constraint in a LP or MILP

Having all the approaches explained in the blog called "OR in an OB World" (this address) in my mind, I would like to ask the following question: What is the best practice to make a constraint linear ...