Long Trieu | Searcharxiv

arXiv2017

A Frank-Wolfe Based Branch-and-Bound Algorithm for Mean-Risk Optimization

We present an exact algorithm for mean-risk optimization subject to a budget constraint, where decision variables may be continuous or integer. The risk is measured by the covariance matrix and weighted by an arbitrary monotone function, which allows to model risk-aversion in a very individual way. We address this class of convex mixed-integer minimization problems by designing a branch-and-bound algorithm, where at each node, the continuous relaxation is solved by a non-monotone Frank-Wolfe type algorithm with away-steps. Experimental results on portfolio optimization problems show that our approach can outperform the MISOCP solver of CPLEX 12.6 for instances where a linear risk-weighting function is considered.

math.OC↗

arXiv2015

A Feasible Active Set Method with Reoptimization for Convex Quadratic Mixed-Integer Programming

We propose a feasible active set method for convex quadratic programming problems with non-negativity constraints. This method is specifically designed to be embedded into a branch-and-bound algorithm for convex quadratic mixed integer programming problems. The branch-and-bound algorithm generalizes the approach for unconstrained convex quadratic integer programming proposed by Buchheim, Caprara and Lodi to the presence of linear constraints. The main feature of the latter approach consists in a sophisticated preprocessing phase, leading to a fast enumeration of the branch-and-bound nodes. Moreover, the feasible active set method takes advantage of this preprocessing phase and is well suited for reoptimization. Experimental results for randomly generated instances show that the new approach significantly outperforms the MIQP solver of CPLEX 12.6 for instances with a small number of constraints.

math.OC↗