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An O(n 3 L) primal—dual potential reduction algorithm for solving convex quadratic programs

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Abstract

In this paper we combine partial updating and an adaptation of Anstreicher's safeguarded linesearch of the primal—dual potential function with Kojima, Mizuno and Yoshise's potential reduction algorithm for the linear complementarity problem to obtain an O(n 3 L) algorithm for convex quadratic programming. Our modified algorithm is a long step method that requires at most O(\(\sqrt n\) L) steps.

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Authors and Affiliations

  1. Department of Industrial Engineering and Operations Research, Columbia University, Seeley W. Mudd Building, 10027, New York, NY, USA

    Donald Goldfarb

  2. BARRA, 1995 University Ave, Berkeley, CA, USA

    Shucheng Liu

Authors
  1. Donald Goldfarb
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  2. Shucheng Liu
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Additional information

This research was supported in part by ONR Contract N-00014-87-K0214, NSF Grants DMS-85-12277 and DMS-91-06195.

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Goldfarb, D., Liu, S. An O(n 3 L) primal—dual potential reduction algorithm for solving convex quadratic programs. Mathematical Programming 61, 161–170 (1993). https://doi.org/10.1007/BF01582145

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  • DOI: https://doi.org/10.1007/BF01582145

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