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...

Investors with small portfolios, or a limited number of securities in their portfolios, may benefit from a new portfolio optimization method. Placing a limit on the number of assets in a portfolio turns the ordinary mean variance portfolio optimization problem into a challenging puzzle, especially for larger investment universes. In response, practitioners typically employ either enumerative methods, such as branch-and-bound based on quadratic programming relaxation, or heuristic methods....