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i am currently trying to minimize a function with linear inequality and equality constraints. The Problem is that fmincon (MATLAB Tool) can not find a feasible solution. I already tried to do everything from the list: http://de.mathworks.com/help/optim/ug/when-the-solver-fails.html

Maybe the problem is too large for fmincon. I have to solve with ~3300 inequality constraints and 1 equality constraint. The function is a scalar function with 9 variables: S = sum((X_i-1)^2)

In addition to that, i have to solve this problem ~3300 times (number of inequality constraints). So i can not wait too long for one minimization.

I do not know if fmincon is not capable of this problem and would like to her suggestions for alternative optimization tools. MATLAB would be perfect (or C/C++). And i can not afford to purchase any software.

I hope you can help me

Toffikeks
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So you want to solve a quadratic problem with 3300 equations and you expect it to be fast. I think the real problem isn't the programming, but that you'll have to do more analysis of your problem rather than just using brute force.

If you think that there is nothing more to do, one idea could be to use some heuristics, but then you aren't sure that you get the exact solution. Using Heuristics will require that you know your problem, such that you can apply the correct one.

Another possibility is to try and figure out which constraints are really going to be the ones that matter. Maybe you can identify 10 such constraints, solve the problem with those, and then apply one additional constraint after another with the previous solution as initial guess and then hoping that the solution not suddenly change.

Nicky Mattsson
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