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I am currently trying to optimize an equation that contains 4 variables. It is nonlinear and non-convex.

In mathematica, to optimize this equation, I take the partial derivative of each variables, then set it to zero and solve it together. It is running for 20 hours now, and it looks the CAD tool is frozen. I also try using the Lagrange, and it just doesn't solve.

I have talked to some friends and they suggest me to go to this website: http://en.wikipedia.org/wiki/List_of_optimization_software

Because I am new to those software, I am wondering if any of them solve the optimization symbolically?

Michael Grant
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kuku
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  • It would seem that you could be more specific about your optimization problem. You have a function (not an "equation") of four variables. What is the domain? You said you took the partial derivatives with respect to each variable, so presumably the function is defined in symbolic form. – hardmath Aug 06 '14 at 02:05
  • Four variables is very small, even for a nonconvex problem. Gradient descent or Newton's method might be able to find a satisfactory local minimum extremely quickly. You could also try a brute force search, trying say $100$ possible values for each of your four variables. Can you write your optimization problem explicitly? – littleO Aug 06 '14 at 02:06
  • You need to ask a much more precise question. If you're using Mathematica, you might consider asking on mathematica.se but, again, you must reference a specific example. Is there any chance you're using the Minimize command command when NMinimize would be more appropriate? – Mark McClure Aug 06 '14 at 02:25

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If your function is a multivariate polynomial, there may be some chance of a symbolic solution. Otherwise (and in the absence of special features such as symmetry) there's not much chance. Numerical methods are the way to go.
But I'd try a numerical optimiser rather than solving for the partial derivatives. In Maple it would be Minimize in the Optimization package. In Matlab you might try fminsearch. I don't know about Mathematica.

Robert Israel
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