In this paper we consider the problem of "nding the e$cient frontier associated with the standard mean}variance portfolio optimisation model. We extend the standard model to include cardinality constraints that limit a portfolio to have a speci"ed number of assets, and to impose limits on the proportion of the portfolio held in a given asset (if any of the asset is held). We illustrate the di!e...

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...

Abstract Sparse PCA methods are used to overcome the difficulty of interpreting solution obtained from PCA. However, constraining obtain sparse solutions is an intractable problem, especially in a high-dimensional setting. Penalized due their computational tractability. Nevertheless, recent developments permit efficiently obtaining good cardinality-constrained problems allowing comparison betwe...

modern portfolio theory is based on harry markowitz's 1952 work on mean-variance portfolios. he stated that a rational investor should either maximize his expected return for a given level of risk, or minimize his risk for a given expected return. in this study the markowitz model with cardinality constraints was studied. we extend the standard model to include cardinality constraints that...

The traditional quadratic programming approach to portfolio optimisation is difficult to implement when there are cardinality constraints. Recent approaches to resolving this have used heuristic algorithms to search for points on the cardinality constrained frontier. However, these can be computationally expensive when the practitioner does not know a priori exactly how many assets they may des...