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1500 questions
33
votes
12 answers
MATLAB vs. Python in industry
I am a beginning PhD student in math, and I would like to focus on optimization. I am learning programming for the first time, and I have written out some rudimentary optimization algorithms in both Python and MATLAB. From my very limited…
Blue
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33
votes
4 answers
Why are integer minimax problems hard?
Problems that have a minimax-type structure are notoriously hard to solve. For example, the $p$-median problem from facility location (choose $p$ facilities to minimize demand-weighted distance to customers) does not have a minimax…
LarrySnyder610
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32
votes
5 answers
Cubic programming and beyond?
It is almost inevitable in Operations Research to come across linear or quadratic programming problems. The overall structures of these problems are below: \begin{align}\begin{array}{ll}
\sf{Linear}\\
\max & \bf c^\top x\\
\text{s.t.} & A\bf x\le b…
ə̷̶̸͇̘̜́̍͗̂̄︣͟
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32
votes
8 answers
Modeling floor function exactly
Suppose we want to enforce a constraint
$$
y=\lfloor{x}\rfloor
$$
where $x$ is some continuous variable. One option is to use
$$
x-1\leq{y}\leq{x},\quad y\in\mathbb{Z},
$$
which fails on the edge case $x\in\mathbb{Z}$. One way around this which…
David M.
- 2,077
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32
votes
3 answers
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 using one or more linear constraints?
LarrySnyder610
- 13,141
- 3
- 41
- 105
32
votes
2 answers
Make a living as a math programming freelancer?
I would like to know how the (job) market for operations research works. My dream would be to work as a freelancer in the area of math programming. I have a PHD and several years of proven experience in programming, modeling, bioinformatics, and…
hplan
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31
votes
5 answers
Optimization terminology: "Exact" v. "Approximate"
In optimization literature, I frequently see solution methods termed "exact" or "approximate". (I use the term "method" here because I suspect exactness, or its lack, is a function of both algorithm and model.) My understanding is that "exact"…
prubin
- 39,078
- 3
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- 104
31
votes
4 answers
"Best practices" for formulating MIPs
Often there are many alternatives ways for formulating a MIP. For example:
The model contains inequality constraints that must hold with equality in an optimal solution.
The model contains continuous variables that will necessarily be integer in…
Rolf van Lieshout
- 2,325
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31
votes
3 answers
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 feasible solutions, and your solver of choice:
For what theoretical and/or practical (implementation-specific?) reason(s) would you…
fbahr
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31
votes
2 answers
When are Decision Diagrams the right way to model and solve a problem?
Decision Diagrams are a relatively new approach to solving difficult combinatorial optimization problems. See http://www.andrew.cmu.edu/user/vanhoeve/mdd/ for some information on this approach. Are there any general rules that can help identify…
Michael Trick
- 2,362
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30
votes
17 answers
Recommended books/materials for practical applications of Operations Research in industry
I have a Masters' degree in Mathematics. I've very fair understanding of methods and techniques of Operations Research. I am looking for a good book/material where I can see a lot of examples on Math Model be it Integer Programming or Linear…
pampu1990
- 417
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- 5
29
votes
4 answers
What are the advantages of commercial solvers like Gurobi or Xpress over open source solvers like COIN-OR or CVXPY?
I come from an ML background, and occasionally have to dive into the OR world. I am trying to figure out whether I need to purchase a commercial solver license for a certain problem set.
In the ML world, open source libraries like Tensorflow,…
Skander H.
- 2,139
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29
votes
3 answers
What is the difference between integer programming and constraint programming?
At first glance both approaches appear to be very similar.
What are the major differences between integer programming and constraint programming?
YukiJ
- 2,023
- 12
- 39
29
votes
4 answers
How to avoid having your optimization models rusting?
When designing optimization models for external organizations, I have witnessed the following:
We design an optimization model for a given problem.
We fine-tune it based on a portfolio of representative instances.
The model starts being used in…
Renaud M.
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29
votes
5 answers
Which GPUs to get for Mathematical Optimization (if any)?
The Machine Learning community has largely benefited from modern GPUs and several large companies are investing in new dedicated hardware.
Unfortunately, academic and commercial mathematical optimization solvers still lack support for GPUs. They…
Stefano Gualandi
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