Low order-value approach for solving VaR-constrained optimization problems

In low order-value optimization (LOVO) problems the sum of the r smallest values of a finite sequence of q functions is involved as the objective to be minimized or as a constraint. The latter case is considered in the present paper. Portfolio optimization problems with a constraint on the admissible Value-at-Risk (VaR) can be modeled in terms of LOVOconstrained minimization. Different algorithms for practical solution of this problem will be presented. Using these techniques, portfolio optimization problems with transaction costs will be solved.