Minimization of the root of a quadratic functional under a system of affine equality constraints with application to portfolio management
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.
scientific article; zbMATH DE number 5315432
scientific article