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An Exterior Newton Method for Strictly Convex Quadratic Programming

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Abstract

We propose an exterior Newton method for strictly convex quadratic programming (QP) problems. This method is based on a dual formulation: a sequence of points is generated which monotonically decreases the dual objective function. We show that the generated sequence converges globally and quadratically to the solution (if the QP is feasible and certain nondegeneracy assumptions are satisfied). Measures for detecting infeasibility are provided. The major computation in each iteration is to solve a KKT-like system. Therefore, given an effective symmetric sparse linear solver, the proposed method is suitable for large sparse problems. Preliminary numerical results are reported.

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Authors and Affiliations

  1. Department of Computer Science and Center for Applied Mathematics, Cornell University, Ithaca, NY, 14853, USA

    Thomas F. Coleman

  2. Department of Mathematics, University of North Texas, Denton, TX, 76203, USA

    Jianguo Liu

Authors
  1. Thomas F. Coleman
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  2. Jianguo Liu
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Coleman, T.F., Liu, J. An Exterior Newton Method for Strictly Convex Quadratic Programming. Computational Optimization and Applications 15, 5–32 (2000). https://doi.org/10.1023/A:1008773230148

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