Computational study of a family of mixed-integer quadratic programming problems
Mathematical Programming: Series A and B
Heuristics for cardinality constrained portfolio optimisation
Computers and Operations Research
Integrating SQP and Branch-and-Bound for Mixed Integer Nonlinear Programming
Computational Optimization and Applications
A local relaxation approach for the siting of electrical substation
Computational Optimization and Applications
Lagrangian relaxation procedure for cardinality-constrained portfolio optimization
Optimization Methods & Software
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The NP-hard nature of cardinality constrained mean-variance portfolio optimization problems has led to a number of different algorithms with varying degrees of success in reaching optimality given limited computational resources and under the presence of strict time constraints present in practice. The proposed local relaxation algorithm explores the inherent structure of the objective function. It solves a sequence of small, local, quadratic-programs by first projecting asset returns onto a reduced metric space, followed by clustering in this space to identify sub-groups of assets that best accentuate a suitable measure of similarity amongst different assets. The algorithm can either be cold started using a suitable heuristic method such as the centroids of initial clusters or be warm started based on the last output. Results, using a basket of up to 3,000 stocks and with different cardinality constraints, indicates that the proposed algorithm can lead to significant performance gain over popular branch-and-cut methods. One key application of this algorithm is in dealing with large scale cardinality constrained portfolio optimization under tight time constraint, such as for the purpose of index tracking or index arbitrage at high frequency.