Minimization of Increasing Co-radiant Functions with Branch and Bound Method and Its Application in Portfolio Optimization

Document Type : Original Paper

Authors

1 Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.

2 Department of Mathematics, Faculty of Sciences and Modern Technologies, Graduate University of Advanced Technology, Kerman, Iran.

Abstract

The branch and bound algorithm is a widespread method for global optimization. This algorithm partitions the feasible set of the optimization problem through a branching method and then calculates an upper bound and a lower bound for each member of the partition using a bounding method. Finally, the branch and bound method compares the obtained bounds and the objective function values ​​with each other and removes the members of the partition that do not contain an optimal point. In this paper, the branch and bound algorithm for optimizing increasing co-radiant functions on subsets of $\mathbb{R}_+^n$ which are presented in the form of the intersection of a half-space with a simplex (the purpose of considering such feasible sets is to examine a model of financial mathematics, called the mean-standard deviation model). We use the concept of abstract convexity to increase co-radiant functions for bounding (finding lower bounds). In the end, as an application of this optimization problem, we propose the mean-standard deviation model of portfolio optimization and solve it with the branch and bound method.

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History

  • Receive Date: 09 September 2023
  • Revise Date: 11 August 2024
  • Accept Date: 10 September 2024

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