8
votes
Fast way to repeatedly solve many similar LPs/QPs in parallel
The OPTMODEL modeling language in SAS (disclaimer: I work at SAS) supports two features for solving independent optimization (LP or otherwise) problems concurrently:
The COFOR loop, which ...
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6
votes
Fast way to repeatedly solve many similar LPs/QPs in parallel
A very easy way to do this is to use multiprocessing alongside cvxpy. It won't be fastest possible, but since you want to stick ...
- 613
6
votes
Conditions for minima in calculus of variations
It is possible to apply the notions of stationary points and the second derivative of a function to functionals.
For $|\varepsilon|\ll1$ and and a differentiable function $h$, we can write, using ...
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6
votes
Conditions for minima in calculus of variations
Coming from the world of optimal control, I tend to view the calculus of variations from a Pontryagin point of view. The conditions stated by Pontryagin are necessary, and sufficient under certain ...
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6
votes
Accepted
Fast way to repeatedly solve many similar LPs/QPs in parallel
After a good bit of experimentation based on the ideas posted, here was my solution:
Do as many matrix multiplications up front using pytorch on the GPU to simplify the problem. This means two things....
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5
votes
Fast way to repeatedly solve many similar LPs/QPs in parallel
If I understand this correctly, you are solving 900 QPs (one for each combination of $i$ and $j$), tweaking the parameters, then solving all 900 again (and again). One possibility to try would be hot-...
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5
votes
Accepted
Minimize $\int_0^\infty g'(x)f(x)\,dx$ where $f(x)$ has a log-normal density
Proposition. There is no minimiser.
Proof: An equivalent version of your problem is as follows.
Statement. We wish to minimise $$\int_{-\infty}^\infty xe^{q(x)-x^2}\,dx$$ where $q(x)$ is a strictly ...
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5
votes
Integer Decision Variables Always Forced to Zero in Minimization Problem (MINLP)
You can try adding a constraint forcing one of the affected variable to be nonzero. If the model becomes infeasible, you can try to find the conflicting constraints. If the model stays feasible, this ...
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3
votes
Integer Decision Variables Always Forced to Zero in Minimization Problem (MINLP)
I only skimmed your model so others may be better able to point to the error directly, but here are some reasons this may occur:
Constraints: as you mention, perhaps they're set so that it's not ...
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2
votes
Fast way to repeatedly solve many similar LPs/QPs in parallel
I suggest you consider the Parameterized Fusion API for MOSEK (available in Python). You can use it to construct your model without passing actual data for the parameter values, and then set the ...
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2
votes
Optimize probability parameter in an optimal control problem
Note that $V(O)$ is simply of the form $\sf Q_1/L_1$ where $\sf Q_1$ is a quadratic and $\sf L_1$ is a linear function of $p$. This can be written as ${\sf{L_2}}+c/\sf{L_1}$ where $\sf L_2$ is also ...
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1
vote
How to evaluate the convexity of an optimal control problem?
I suggest to take a look at "Foundations of Optimization" written by Osman Guler and edited by Springer in 2010. The 3rd chapter is wholly dedicated to Variational Principles and in 4.5 &...
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