Skip to main content
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 ...
RobPratt's user avatar
  • 32.8k
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 ...
Robert Bassett's user avatar
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 ...
TheSimpliFire's user avatar
  • 5,432
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 ...
fpacaud's user avatar
  • 1,511
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....
Zach Lee's user avatar
  • 131
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-...
prubin's user avatar
  • 39.6k
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 ...
TheSimpliFire's user avatar
  • 5,432
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 ...
Simon's user avatar
  • 1,142
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 ...
E. Tucker's user avatar
  • 1,317
2 votes
Accepted

Inconsistent solutions to linear optimal control problem

One of the necessary conditions is $L_u = 0$. If you assume that $\mu(t) = 0$, it follows from $L_u = \mu_x(t) + \mu(t) = 0$ that $\mu_x(t) = 0$. Because $u(t)$ can take any value when $\mu_x(t) = 0$, ...
Kevin Dalmeijer's user avatar
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 ...
Utkarsh Detha's user avatar
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 ...
TheSimpliFire's user avatar
  • 5,432
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 &...
marco tognoli's user avatar

Only top scored, non community-wiki answers of a minimum length are eligible