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I would like to consider how to solve the following optimization problem:

$\max x^{T}\mathbf{a}-b\sqrt{x^{T}\Sigma x}\;s.t.x^{T}\mathbf{1}=1$, provided that $b>0$ and $\Sigma$ is positive definite.

I want to solve KKT condition to solve the problem, however, I do not obtain a nice result.

will_cheuk
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1 Answers1

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Are you asking how you can solve this analytically through the KKT conditions? My guess is you cannot, but you use a numerical solver to solve the problem instead.

This is a fairly easy convex optimization problem, and almost any nonlinear solver will solve it without problems. If you want to go fancy, you use a solver specially devoted to problems of this kind (it can be written as a so called SOCP problem)

Johan Löfberg
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