Minimization methods for non-differentiable functions
Minimization methods for non-differentiable functions
Global convergence of the partitioned BFGS algorithm for convex partially separable optimization
Mathematical Programming: Series A and B
Nondifferentiable optimization via smooth approximation: general analytical approach
Annals of Operations Research - Special issue on sensitivity analysis and optimization of discrete event systems
Element-by-Element Preconditioners for Large Partially Separable Optimization Problems
SIAM Journal on Scientific Computing
Interior Methods for Nonlinear Optimization
SIAM Review
Portfolio Selection and Transactions Costs
Computational Optimization and Applications
Robust portfolio selection problems
Mathematics of Operations Research
The Entire Regularization Path for the Support Vector Machine
The Journal of Machine Learning Research
Regularity and well-posedness of a dual program for convex best C1-spline interpolation
Computational Optimization and Applications
Low order-value approach for solving VaR-constrained optimization problems
Journal of Global Optimization
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We consider the fundamental problem of computing an optimal portfolio based on a quadratic mean-variance model for the objective function and a given polyhedral representation of the constraints. The main departure from the classical quadratic programming formulation is the inclusion in the objective function of piecewise linear, separable functions representing the transaction costs. We handle the non-smoothness in the objective function by using spline approximations. The problem is first solved approximately using a primal-dual interior-point method applied to the smoothed problem. Then, we crossover to an active set method applied to the original non-smooth problem to attain a high accuracy solution. Our numerical tests show that we can solve large scale problems efficiently and accurately.