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A Unified Approach to Interior Point Algorithms for Linear Complementarity Problems

  • Kartonierter Einband
  • 120 Seiten
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Following Karmarkar's 1984 linear programming algorithm, numerous interior-point algorithms have been proposed for various mathema... Weiterlesen
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Beschreibung

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.

This monograph presents a study of interior-point algorithms for the linear complementarity problem, known as a mathematical model for primal-dual pairs of linear programs and convex quadratic programs. A large class of potential reduction algorithms is presented in a unified way.

Klappentext

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.



Inhalt
Summary.- The class of linear complementarity problems with P 0-matrices.- Basic analysis of the UIP method.- Initial points and stopping criteria.- A class of potential reduction algorithms.- Proofs of convergence theorems.

Produktinformationen

Titel: A Unified Approach to Interior Point Algorithms for Linear Complementarity Problems
Autor:
EAN: 9783540545095
ISBN: 3540545093
Format: Kartonierter Einband
Herausgeber: Springer Berlin Heidelberg
Anzahl Seiten: 120
Gewicht: 195g
Größe: H235mm x B155mm x T6mm
Jahr: 1991
Untertitel: Englisch
Auflage: 1991

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