Owadally, I. (2012). An improved closed-form solution for the constrained minimization of the root of a quadratic functional. Journal of Computational and Applied Mathematics, 236(17), pp. 4428-4435. doi: 10.1016/j.cam.2012.04.014
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The problem of minimizing the root of a quadratic functional, subject to a system of affine constraints, occurs in investment portfolio selection, insurance risk theory, tomography, and other areas. We provide a solution that improves on the current published solution by being considerably simpler in computational terms. In particular, a succession of partitions and inversions of large matrices is avoided. Our solution method employs the Lagrangian multiplier method and we give two proofs, one of which is based on the solution of a related convex optimization problem. A geometrically intuitive interpretation of the objective function and of the optimization solution is also given.
|Additional Information:||© 2012, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/|
|Uncontrolled Keywords:||Minimization; Root of quadratic functional; Linear constraints; Portfolio selection|
|Subjects:||Q Science > QA Mathematics|
|Divisions:||Cass Business School > Faculty of Actuarial Science & Insurance|
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