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Results tagged with linear-programming
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user 9652
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
Accepted
accelerate convex optimization by proximal projection
There is abundant literature about stuff like this but it can be hard to find the framework that is best suited for your case.
For example there is quite general theory in "Incremental subgradients f …
- 12.7k
1
vote
Continuous Transportation Problem
Regarding your question below the answer of Tapio Rajala: Testing feasibility of $\rho$ simply amounts to checking that
$$\mu_1(A) = \rho(A\times Y),\qquad\text{and}\qquad \mu_2(B) = \rho(X\times B)$ …
- 12.7k
1
vote
Literature request: Function that depends on a linear optimization problem
This is sometimes called the "optimal value function". I remember that Rockafellar/Wets "Variational Analysis" treats this in some generality.
If you could evaluate the function without solving an op …
- 12.7k
3
votes
Accepted
Better alternative to solve quadratic programming for large matrices
Your problem is also convex. Hence, a whole bunch of methods for convex optimization are available. Since projecting onto the constraints is not too difficult (project each row of $A$ onto the simplex …
- 12.7k
1
vote
Accepted
Standard names and methods for this type of fitting minimization
I am not sure if there is a standard name for these type of problems. I would call problems of this type sparse approximation problems because you want to solve a linear equation approximately (assumi …
- 12.7k
2
votes
Accepted
How to minimize l1-norm constrained by "infinity norm"
This work like this: The $\infty$-norm constraints are straigtforward. In the first problem you write
$$
-1 \leq x_i \leq 1
$$
or, more explicitely
$$
x_i\leq 1\\-x_i\leq 1.
$$
One could even just wr …
- 12.7k
2
votes
Integer solution of optimal transport
Yes, this is true and can found, for example in Chapter 7 of the "Handbook of Discrete and Computational Geometry" edited by Csaba D. Toth, Joseph O'Rourke, Jacob E. Goodman (chapter by Alexander Barv …
- 12.7k
1
vote
Reference request: dependence on linear constraints
If you consider general linear programming problems and the solution in dependence on changes in the right hand side, you want to look for sensitivity analysis in linear programming and more specifica …
- 12.7k
58
votes
Accepted
Why are optimization problems often called "programs"?
It may be that this question had been answered here before, but I couldn't find the answer.
Anyway, the answer is given by the person who coined the name itself: George Dantzig wrote in "LINEAR PROGR …
- 12.7k