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Large Scale Optimization pp 411–427Cite as

A Simple, Quadratically Convergent Interior Point Algorithm for Linear Programming and Convex Quadratic Programming

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Abstract

An algorithm for linear programming (LP) and convex quadratic programming (CQP) is proposed, based on an interior point iteration introduced more than ten years ago by J. Herskovits for the solution of nonlinear programming problems. Herskovits’ iteration can be simplified significantly in the LP/CQP case, and quadratic convergence from any initial point can be achieved. Interestingly the linear system solved at each iteration is identical to that of the primal-dual affine scaling scheme recently considered by Monteiro et al. independently of Herskovits’ work. The proposed algorithm, however, uses an iteratively selected step length, different for each component of the dual variable.

This research was supported in part by NSF’s Engineering Research Centers Program No. NSFD-CDR-88-03012 and by NSF grant No. DMC-88-15996.

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References

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Author information

Authors and Affiliations

  1. Electrical Engineering Department and Institute for Systems Research, University of Maryland, College Park, MD, 20742, USA

    André L. Tits

  2. Institute for Systems Research, University of Maryland, College Park, MD, 20742, USA

    Jian L. Zhou

Authors
  1. André L. Tits
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  2. Jian L. Zhou
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Editor information

Editors and Affiliations

  1. Center for Applied Optimization, University of Florida, Gainesville, USA

    W. W. Hager , D. W. Hearn  & P. M. Pardalos ,  & 

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© 1994 Kluwer Academic Publishers

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Tits, A.L., Zhou, J.L. (1994). A Simple, Quadratically Convergent Interior Point Algorithm for Linear Programming and Convex Quadratic Programming. In: Hager, W.W., Hearn, D.W., Pardalos, P.M. (eds) Large Scale Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3632-7_20

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  • DOI: https://doi.org/10.1007/978-1-4613-3632-7_20

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-3634-1

  • Online ISBN: 978-1-4613-3632-7

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