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Results tagged with linear-programming
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user 3816
Linear programming is the study of optimizing a linear function over a set of linear inequalities. The Simplex Method, Ellipsoid Method and Interior Point Method are popular algorithms to solve linear programs.
2
votes
How to implement linear constraints that include several absolute values
Without having more information about the problem, I would suggest to generate the constraints of the +/- form on the fly. Several approaches are possible:
You can solve the problem, generate the vi …
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2
votes
Is it possible to represent non-linear ranking type constraints as equivalent linear constra...
In addition to the binary restrictions, take
$z^1_{ij}(a) \geq z_i(a) + \sum_{b<a} z_j(b) - 1$
and similar for the second equation.
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1
vote
Linear programming with exponentially many constraints and variables
If you have exponentially many variables, but usually, only a few of them are non-zero, you can try Column-Generation or Branch-and-Price.
Having exponentially many variables AND constraints is usua …
- 1,282
1
vote
Constrained vs Unconstrained Optimization
This depends on the kind of non-linearity, especially if these constraints are convex.
It is also possible to try to convert the non-linear constraints into a possibly exponential number of linear co …
- 1,282
1
vote
Accepted
ILP for minimum edge coloring problem
If $c$ is an upper bound for the number of colours (in case of doubt use $|E|$), then you could use binary assigment variables $x_{ie}$ for assigning colour $i$ to edge $e$. Then, for every two edges …
- 1,282
2
votes
Fastest 'Oracle' Algorithm for satisfying a single linear constraint on a convex set?
Actually, I guess that they do not mean that such an oracle always exists. Usually, the argument is of the form: If, for your special problem, you have a quick method of checking if this problem has a …
- 1,282
6
votes
1
answer
255
views
Algorithm that solves every Mixed Integer Linear Program (to optimality)?
Given a Mixed Integer Linear Program with rational coefficients (both for the objective functions and all constraints), is it always possible to solve it algorithmically?
I know that you usually solv …
- 1,282
1
vote
Speed up Linear programming
Following the comment of Robert Israel, I would suggest to solve the problem offline for a large set of different $c$, which are "similar" to those expected in the online optimization. If you store th …
- 1,282
1
vote
Heuristic for choosing n-vectors from n-sets
First of all, I would suggest to model the problem as Mixed Integer Program and try to solve it with a MIP solver. If it turns out to be to hard because the problem is too large, you can try a heurist …
- 1,282