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a unified approach to interior point algorithms for linear complementarity problems (in English)
Kojima,Megiddo,Noma,Yoshise (Author)
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a unified approach to interior point algorithms for linear complementarity problems (in English) - kojima,megiddo,noma,yoshise
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Synopsis "a unified approach to interior point algorithms for linear complementarity problems (in English)"
following karmarkars 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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