1991
DOI: 10.1007/3-540-54509-3
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A Unified Approach to Interior Point Algorithms for Linear Complementarity Problems

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Cited by 416 publications
(302 citation statements)
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“…can be directly formulated as LCPs. For a comprehensive treatment of LCP theory and practice, we refer the reader to the monographs of Cottle, Pang, and Stone [11] and Kojima et al [13], and for a recent comprehensive treatment of variational inequalities and complementarity problems to the monograph of Facchinei and Pang [12].…”
Section: Introductionmentioning
confidence: 99%
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“…can be directly formulated as LCPs. For a comprehensive treatment of LCP theory and practice, we refer the reader to the monographs of Cottle, Pang, and Stone [11] and Kojima et al [13], and for a recent comprehensive treatment of variational inequalities and complementarity problems to the monograph of Facchinei and Pang [12].…”
Section: Introductionmentioning
confidence: 99%
“…Various IPMs for LO have been successfully generalized to LCPs. Besides the aforementioned monograph of Kojima et al [13], and without any attempt to be complete, we mention a few other relevant references: [2,17,18,28,29,30].…”
Section: Introductionmentioning
confidence: 99%
“…Internal penalty methods, also known as barrier methods, had an explosive development in the last fifteen years, due to the success of interior point methods for linear programming and for linear complementarity problems (see the monographs [10,18,19,25,27,28,33]; see also the extensions to nonlinear programming in [4,9,11,14,15,29]). The first deep study of the path of optimizers, now known as central path, is due to McLinden [21], followed by Bayer and Lagarias [3] and by Megiddo [22], who gave a definitive characterization of the primal-dual central path.…”
Section: Introductionmentioning
confidence: 99%
“…Broader classes of LCPs that are still polynomial include monotone LCPs (i.e. positive semidefinite M ) and a generalization of monotone LCPs based on a type of matrix called P * (κ) [7]. We are also working on stochastic Galerkin methods to reduce the cost of each iteration from O(kn) to O(km) for k, m n.…”
Section: Discussionmentioning
confidence: 99%
“…Projective monotone LCPs-a more general class than strictly monotone projective LCPs-can be solved efficiently with a variant of the unified interior point (UIP) method [7] that requires only O(nk 2 ) operations per UIP iteration [5]. UIP requires only a polynomial number of iteration to get within of the solution.…”
Section: Galerkin Methodsmentioning
confidence: 99%