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I have the below portfolio optimization problem that I need to specify in python (using cvxopt or any other optimization package). I am unable to figure out how to specify a problem containing absolute value in the objective function. The problem tries to minimize the difference between portfolio volatility and a target volatility by optimizing the constituent weights. The problem is expressed as below


    Min |xTΣx – σ2target|

    s.t. 

    1Tx = 1
    x >= 0

where Σ is the covariance matrix, and σtarget is the volatility target (5%, for example)

How do I formulate the above problem in python ? I currently use cvxopt for general QP-type problems.

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Vaibhav Agarwal
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  • Do you need to minimize this specific function? can't you minimize (xΣx – σ²)² ? – pbc1303 May 11 '15 at 20:55
  • yes. that would work as well. is there a way to specify this problem using cvxopt, given that its a higher order polynomial involving a covariance matrix and a constant? – Vaibhav Agarwal May 12 '15 at 02:52

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