Minimize absolute deviation from volatility target - portfolio optimization - Python -


i have below portfolio optimization problem need specify in python (using cvxopt or other optimization package). unable figure out how specify problem containing absolute value in objective function. problem tries minimize difference between portfolio volatility , target volatility optimizing constituent weights. problem expressed below

     min |xtΣx – σ2target|      s.t.       1tx = 1     x >= 0

where Σ covariance matrix, , σtarget volatility target (5%, example)

how formulate above problem in python ? use cvxopt general qp-type problems.


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