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A Unified Approach to Interior Point Algorithms for Linear Complementarity Problems (Paperback, 1991 ed.)
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A Unified Approach to Interior Point Algorithms for Linear Complementarity Problems (Paperback, 1991 ed.)
Series: Lecture Notes in Computer Science, 538
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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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