A simple duality proof in convex quadratic programming with a quadratic constraint, and some applications

Date
2000-07-01
Authors
Pinar, M. C.
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Source Title
European Journa of Operational Research
Print ISSN
0377-2217
Electronic ISSN
Publisher
Elsevier
Volume
124
Issue
1
Pages
151 - 158
Language
English
Type
Article
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Abstract

In this paper a simple derivation of duality is presented for convex quadratic programs with a convex quadratic constraint. This problem arises in a number of applications including trust region subproblems of nonlinear programming, regularized solution of ill-posed least squares problems, and ridge regression problems in statistical analysis. In general, the dual problem is a concave maximization problem with a linear equality constraint. We apply the duality result to: (1) the trust region subproblem, (2) the smoothing of empirical functions, and (3) to piecewise quadratic trust region subproblems arising in nonlinear robust Huber M-estimation problems in statistics. The results are obtained from a straightforward application of Lagrange duality. Ó 2000 Elsevier Science B.V. All rights reserved.

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Keywords
Lagrange Duality, Convex Quadratic Programming With A Convex Quadratic Constraint, Ill-posed Least Squares Problems, Trust Region Subproblems
Citation
Published Version (Please cite this version)