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140122 ||| eng |
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|a 9783540384267
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|a Kojima, Masakazu
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| 245 |
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|a A Unified Approach to Interior Point Algorithms for Linear Complementarity Problems
|h Elektronische Ressource
|c by Masakazu Kojima, Nimrod Megiddo, Toshihito Noma, Akiko Yoshise
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| 250 |
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|a 1st ed. 1991
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| 260 |
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|a Berlin, Heidelberg
|b Springer Berlin Heidelberg
|c 1991, 1991
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| 300 |
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|a VIII, 112 p
|b online resource
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| 505 |
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|a 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
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| 653 |
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|a Numerical Analysis
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| 653 |
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|a Calculus of Variations and Optimization
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| 653 |
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|a Control theory
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| 653 |
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|a Systems Theory, Control
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| 653 |
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|a System theory
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| 653 |
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|a Numerical analysis
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| 653 |
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|a Applications of Mathematics
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| 653 |
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|a Mathematics
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| 653 |
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|a Mathematical optimization
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| 653 |
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|a Calculus of variations
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| 700 |
1 |
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|a Megiddo, Nimrod
|e [author]
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| 700 |
1 |
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|a Noma, Toshihito
|e [author]
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| 700 |
1 |
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|a Yoshise, Akiko
|e [author]
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| 041 |
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7 |
|a eng
|2 ISO 639-2
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| 989 |
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|b SBA
|a Springer Book Archives -2004
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| 490 |
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|a Lecture Notes in Computer Science
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| 028 |
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|a 10.1007/3-540-54509-3
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| 856 |
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|u https://doi.org/10.1007/3-540-54509-3?nosfx=y
|x Verlag
|3 Volltext
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| 082 |
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|a 519
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| 520 |
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|a 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
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