A Unified Approach to Interior Point Algorithms for Linear Complementarity Problems

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Springer Science & Business Media, Sep 25, 1991 - Language Arts & Disciplines - 108 pages
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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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Contents

I
1
II
7
IV
10
V
15
VI
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VII
25
IX
26
X
30
XVI
53
XVII
59
XIX
68
XX
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XXI
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XXIII
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XXIV
87
XXV
88

XI
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XII
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XIV
39
XV
48
XXVI
91
XXVII
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XXVIII
103
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