A Unified Approach to Interior Point Algorithms for Linear Complementarity Problems

  • Authors
  • Masakazu Kojima
  • Nimrod Megiddo
  • Toshihito Noma
  • Akiko Yoshise

Part of the Lecture Notes in Computer Science book series (LNCS, volume 538)

About this book


Following Karmarkar's 1984 linear programming algorithm, numerous interior-point algorithms have been proposed for various mathematical programming problems such as linear programming, convex quadratic programming and convex programming in general. This monograph presents a study of interior-point algorithms for the linear complementarity problem (LCP) which is known as a mathematical model for primal-dual pairs of linear programs and convex quadratic programs. A large family of potential reduction algorithms is presented in a unified way for the class of LCPs where the underlying matrix has nonnegative principal minors (P0-matrix). This class includes various important subclasses such as positive semi-definite matrices, P-matrices, P*-matrices introduced in this monograph, and column sufficient matrices. The family contains not only the usual potential reduction algorithms but also path following algorithms and a damped Newton method for the LCP. The main topics are global convergence, global linear convergence, and the polynomial-time convergence of potential reduction algorithms included in the family.


Complementarity Innerer-Punkt-Methode Interior-Point Method Komplementarität Linear Programming Lineares Programmieren Mathematics of Computing Mathematik der Informationsverarbeitung Optimierung algorithms linear optimization optimization

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 1991
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-54509-5
  • Online ISBN 978-3-540-38426-7
  • Series Print ISSN 0302-9743
  • Series Online ISSN 1611-3349
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