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

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      Author
      Pinar, M. C.
      Date
      2000-07-01
      Source Title
      European Journa of Operational Research
      Print ISSN
      0377-2217
      Publisher
      Elsevier
      Volume
      124
      Issue
      1
      Pages
      151 - 158
      Language
      English
      Type
      Article
      Item Usage Stats
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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.
      Keywords
      Lagrange Duality
      Convex Quadratic Programming With A Convex Quadratic Constraint
      Ill-posed Least Squares Problems
      Trust Region Subproblems
      Permalink
      http://hdl.handle.net/11693/13577
      Published Version (Please cite this version)
      http://dx.doi.org/10.1016/S0377-2217(99)00173-3
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