Lagrangian relaxation procedure for cardinality-constrained portfolio optimization

Abstract

This paper studies a portfolio-selection problem subject to a cardinality constraint, that is, the number of securities in a portfolio is restricted to a certain limit. The problem is formulated as a cardinality-constrained quadratic programming problem, and a dedicated Lagrangian relaxation method is developed. In contrast to many existing Lagrangian relaxation methods, the approach presented in the paper is able to take advantage of the special structure of the objective function rather than the special structure of the constraints. The algorithm developed here has been applied to track the major market indices, such as the S&P 500, S&P 100, FTSE 100, and FTSE 250, using real data, and the computational results are promising.