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Let me start saying that I am by no means expert in optimization, so any suggestion would be greatly appreciated. I have a non-convex quadratic optimization problem for which I need a solver. I myself am used to working with the modelling language CVXPY, using some of the default solvers there (ECOS, CVXOPT,...) so something similar to it would be great. I cannot use cvxpy on this problem because it is only suitable for convex optimization problems.

After googling, I saw some people recommending Pyomo, saying it could deal with non convex problems, but my problem requires matrix algebra, and as far as I know, Pyomo does not include matrix algebra capabilities. So I would require a non convex modeling language or solver for non convex quadratic problems.

The type of problem I am actually interested in solving has the following structure:

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where wis the vector variable to be optimized, Xis a known data matrix and tis a prespecified parameter value.

Álvaro Méndez Civieta
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  • Pyomo+Couenne can handle this (I don't understand your point that it would need matrix algebra -- the notation is different but it surely can express this problem quite easily). Also, Gurobi can solve nonconvex quadratic problems. – Erwin Kalvelagen Dec 04 '20 at 02:16
  • Thank you for your answer. Having no matrix algebra makes the process of changing the objectvie function quite cumbersome. I can code in pyomo the above function, but if instead of (X.T@X) I had to maximize over (say) (Y.T@X.T)@(X@Y) I would need to redefine the whole equation in pyomo. This process is much simpler using matrix algebra.I will have a look into Gurobi. – Álvaro Méndez Civieta Dec 04 '20 at 08:24

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