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A Frank-Wolfe Based Branch-and-Bound Algorithm for Mixed-Integer Portfolio Optimization

Christoph Buchheim (christoph.buchheim***at***tu-dortmund.de)
Marianna De Santis (marianna.de.santis***at***math.tu-dortmund.de)
Francesco Rinaldi (rinaldi***at***math.unipd.it)
Long Trieu (long.trieu***at***math.tu-dortmund.de)

Abstract: We address the solution of a large class of convex mixed-integer nonlinear programming problems. The model we are considering generalizes problems that are commonly considered in portfolio optimization, such as the risk-averse capital budgeting problem. In our generalization we allow to take into account integer and continuous variables as well as an arbitrary weighting of the risk. In order to exactly solve our model, we propose a branch-and-bound method based on the computation of dual bounds via the solution of the primal relaxation. A Frank-Wolfe type algorithm is devised for solving the continuous relaxation at every node of the branch-and-bound tree. A numerical evaluation on real-world instances, including a comparison with CPLEX 12.6, is presented.

Keywords: mixed integer programming, portfolio optimization, global optimization

Category 1: Integer Programming ((Mixed) Integer Nonlinear Programming )


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Entry Submitted: 07/21/2015
Entry Accepted: 07/21/2015
Entry Last Modified: 07/22/2015

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