Minimization of the root of a quadratic functional under a system of affine equality constraints with application to portfolio management
type: Item
instance of: scholarly article
title: Minimization of the root of a quadratic functional under a system of affine equality constraints with application to portfolio management
zbMATH Open document ID: 1152.65067
author: Zinoviy Landsman
published in: Journal of Computational and Applied Mathematics
publication date: 2008-08-22T00:00:00Z
review text: This work is an extension of the author's precessing work [ibid. 216, No. 2, 319--327 (2008; Zbl 1158.65324)] where the root of a quadratic functional is minimized subject to one affine constraint. Here \(m\) constraints are allowed, such that as example the Markowitz optimal portfolio is among the set of the discussed problems. In the main part proofs are given for the positive definiteness of a reduced system matrix that is derived from a nullspace method for the solution of the optimization problem. Thereafter the existence of a finite solution is proved and an analytical formula is derived. In the last section the exact solution is shown as example of the problem with one constraint, the formula coincides with the prior work. Further the portfolio optimization example is discussed again, the previously defined matrices, vectors and the solution expression are used with realistic numbers and show how the method is applied.
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 90C25
Mathematics Subject Classification ID: 91G10
zbMATH DE Number: 5315432
zbMATH Keywords: root of quadratic functional
zbMATH Keywords: minimization
zbMATH Keywords: linear equality constraints
zbMATH Keywords: optimal portfolio
zbMATH Keywords: numerical example
reviewed by: M. D. Korzec
MaRDI profile type: Publication
full work available at URL: j.cam.2007.09.023
OpenAlex ID: W2089104804
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DOI: 10.1016/J.CAM.2007.09.023
description: scientific article; zbMATH DE number 5315432