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Mathematical Programming

, Volume 65, Issue 1–3, pp 43–72 | Cite as

Global convergence in infeasible-interior-point algorithms

  • Masakazu Kojima
  • Toshihito Noma
  • Akiko Yoshise
Article

Abstract

This paper presents a wide class of globally convergent interior-point algorithms for the nonlinear complementarity problem with a continuously differentiable monotone mapping in terms of a unified global convergence theory given by Polak in 1971 for general nonlinear programs. The class of algorithms is characterized as: Move in a Newton direction for approximating a point on the path of centers of the complementarity problem at each iteration. Starting from a strictly positive but infeasible initial point, each algorithm in the class either generates an approximate solution with a given accuracy or provides us with information that the complementarity problem has no solution in a given bounded set. We present three typical examples of our interior-point algorithms, a horn neighborhood model, a constrained potential reduction model with the use of the standard potential function, and a pure potential reduction model with the use of a new potential function.

Keywords

Monotone complementarity problem Interior-point algorithm Potential reduction algorithm Infeasibility Global convergence 

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Copyright information

© The Mathematical Programming Society, Inc 1994

Authors and Affiliations

  • Masakazu Kojima
    • 1
  • Toshihito Noma
    • 2
  • Akiko Yoshise
    • 3
  1. 1.Department of Information SciencesTokyo Institute of TechnologyTokyoJapan
  2. 2.Ships Division, Equipment BureauDefense AgencyTokyoJapan
  3. 3.Institute of Socio-Economic PlanningUniversity of TsukubaTsukuba, IbarakiJapan

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