An improved closed-form solution for the constrained minimization of the root of a quadratic functional

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 i...

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Bibliographic Details
Published inJournal of computational and applied mathematics Vol. 236; no. 17; pp. 4428 - 4435
Main Author Owadally, Iqbal
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.11.2012
Subjects
Computation
Exact solutions
Linear constraints
Mathematical analysis
Mathematical models
Matrices
Minimization
Optimization
Portfolio selection
Risk
Root of quadratic functional
Roots
Minimization
Portfolio selection
Root of quadratic functional
Linear constraints
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Summary: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.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2012.04.014