Look at Scipy:

https://docs.scipy.org/doc/scipy/reference/optimize.minimize-slsqp.html

For quadratic unconstrained and constrained optimization problems in Python, there are several packages you can consider. Here are a few well-documented and actively developed ones:

These packages should provide you with a good starting point for solving your quadratic optimization problem with constraints in Python. Make sure to review their documentation and examples to determine which one suits your needs best.

Additionally, you may find it helpful to explore related topics such as quadratic programming, mixed-integer programming, and constraint programming. The documentation for each package often includes tutorials, examples, and links to further resources.

Best of luck

Ramin Ekhteiari Salmas , thanks for your answer. It really does the job but in my case I have binary optimization, so the x is a vector with binary vars to optimize.. I don't know how scipy handles it. & it's not working fast enough :))

E.g. my x has 2500 .. 10000 variables to optimize + several thousands of constraints to add. Maybe you also had some experience with other solvers?

I can assist you better if you provide your objective function.

In the current case, Ramin Ekhteiari Salmas

I have a simple equation

Ax = b,

where A is a given matrix, b is also a given vector, x- is a binary vector of solutions,

trying to optimize ||Ax-b||^2 , where x is binary.

s.t.

sum(x) == K,

K is some known constant

+ inequality constraints,

Cx 0,

s.t.

sum(x) == K,

Cx

Have you ever tried the pyqubo Python library?

https://pyqubo.readthedocs.io/en/latest/getting_started.html

thank you Ramin Ekhteiari Salmas , now using their samplers & QUBO models, have some preliminary results. For small-sized problems you can try to solve it locally using stochastic approach and SimulatedAnnealing, but for large-scaled - I have used only CQM from DWave. It works fine, costs a lot.

it seems that under the hood it splits a large problem into parts and solve it separately in parallel and then all the results are combined into one solution..

Maybe there is some solver that can be tuned to solve QUBO problem? Some SimulatedAnnealing but more robust and e.g. - you can give some initial guess for solver, or change the temp. schedule.. because now I can see that results are almost random.. Only giving to solver a lot of tries you can get some applicable results.