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A Unified Approach to Interior Point Algorithms for Linear Complementarity Problems [electronic resource] /
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.
| Main Authors: | , , , , |
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| Format: | Texto biblioteca |
| Language: | eng |
| Published: |
Berlin, Heidelberg : Springer Berlin Heidelberg,
1991
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| Subjects: | Mathematics., Applied mathematics., Engineering mathematics., System theory., Numerical analysis., Calculus of variations., Applications of Mathematics., Numerical Analysis., Systems Theory, Control., Calculus of Variations and Optimal Control; Optimization., |
| Online Access: | http://dx.doi.org/10.1007/3-540-54509-3 |
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