A Unified Approach to Interior Point Algorithms for Linear Complementarity Problems

di Masakazu Kojima (Autore)

Nimrod Megiddo (Autore)

Toshihito Noma (Autore)

Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, 1991

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.

• Autore: Masakazu Kojima, Nimrod Megiddo, Toshihito Noma
• Editore: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
• Collana: Lecture Notes in Computer Science
• Anno: 1991
• Rilegatura: Paperback / softback
• Pagine: 112 p.
• Dimensioni: 233 x 155 mm
• EAN: 9783540545095

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