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

In: Large Scale Optimization

Author

Listed:
  • André L. Tits

    (University of Maryland, Electrical Engineering Department and Institute for Systems Research)

  • Jian L. Zhou

    (University of Maryland, Institute for Systems Research)

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.

Suggested Citation

  • André L. Tits & Jian L. Zhou, 1994. "A Simple, Quadratically Convergent Interior Point Algorithm for Linear Programming and Convex Quadratic Programming," Springer Books, in: W. W. Hager & D. W. Hearn & P. M. Pardalos (ed.), Large Scale Optimization, pages 411-427, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4613-3632-7_20
    DOI: 10.1007/978-1-4613-3632-7_20
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