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Error Bounds for Monotone Linear Complementarity Problems
, 1985
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An Infeasible Interior Point Method for the Monotone Linear Complementarity Problem
"... Abstract. Linear complementarity problem noted (LCP) becames in present the subject of many reseach interest because it arises in many areas and it includes the two important domains in optimization:the linear programming (LP) and the convex quadratic (CQP) programming. So the researchers aims to ex ..."
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to extend the results obtained in (LP) and (CQP) to (LCP). Differents classes of methods are proposed to solve (LCP) inspired from (LP) and (CQP). In this paper, we present an infeasible interior point method to solve the monotone linear complementarity problem. Comparative results of this method
Convergence of Interior Point Algorithms for the Monotone Linear Complementarity Problem
, 1994
"... The literature on interior point algorithms shows impressive results related to the speed of convergence of the objective values, but very little is known about the convergence of the iterate sequences. This paper studies the horizontal linear complementarity problem, and derives general convergence ..."
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Cited by 25 (4 self)
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The literature on interior point algorithms shows impressive results related to the speed of convergence of the objective values, but very little is known about the convergence of the iterate sequences. This paper studies the horizontal linear complementarity problem, and derives general
An Application Of Carver's Theorem To Monotone Linear Complementarity Problems
"... h is sufficient for the boundedness of the solution set F , see Mangasarian [3]. Corollary 3 in Ye [6] states that the existence of such x and s is also necessary in the case of monotone LCPs with a socalled negative qvalue. To see that it is necessary in general, suppose that there exist no ..."
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h is sufficient for the boundedness of the solution set F , see Mangasarian [3]. Corollary 3 in Ye [6] states that the existence of such x and s is also necessary in the case of monotone LCPs with a socalled negative qvalue. To see that it is necessary in general, suppose that there exist
Fast solutions to projective monotone linear complementarity problems. arXiv:1212.6958
, 2012
"... iv ..."
Key words. Monotone Linear Complementarity Problems, Convex Quadratic Programming, KarushKuhnTucker Conditions
"... Our work is related to that of Robinson [7,8], who discusses methods for reducing variational inequalities (possibly nonlinear and nonmonotone) that have certain structural properties. There is a subclass of problems for which the reduction techniques discussed here and those of Robinson are identic ..."
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Our work is related to that of Robinson [7,8], who discusses methods for reducing variational inequalities (possibly nonlinear and nonmonotone) that have certain structural properties. There is a subclass of problems for which the reduction techniques discussed here and those of Robinson are identical. We mention some problems of this type in Section 4 and discuss the relationship between the reduction techniques in more detail there.
The Extended Linear Complementarity Problem
, 1993
"... We consider an extension of the horizontal linear complementarity problem, which we call the extended linear complementarity problem (XLCP). With the aid of a natural bilinear program, we establish various properties of this extended complementarity problem; these include the convexity of the biline ..."
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Cited by 776 (28 self)
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We consider an extension of the horizontal linear complementarity problem, which we call the extended linear complementarity problem (XLCP). With the aid of a natural bilinear program, we establish various properties of this extended complementarity problem; these include the convexity
Interiorpoint Methods
, 2000
"... The modern era of interiorpoint methods dates to 1984, when Karmarkar proposed his algorithm for linear programming. In the years since then, algorithms and software for linear programming have become quite sophisticated, while extensions to more general classes of problems, such as convex quadrati ..."
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Cited by 603 (15 self)
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, monotone linear complementarity, and convex programming over sets that can be characterized by selfconcordant barrier functions.
LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
 ACM Trans. Math. Software
, 1982
"... An iterative method is given for solving Ax ~ffi b and minU Ax b 112, where the matrix A is large and sparse. The method is based on the bidiagonalization procedure of Golub and Kahan. It is analytically equivalent to the standard method of conjugate gradients, but possesses more favorable numerica ..."
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Cited by 649 (21 self)
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gradient algorithms, indicating that I~QR is the most reliable algorithm when A is illconditioned. Categories and Subject Descriptors: G.1.2 [Numerical Analysis]: ApprorJmationleast squares approximation; G.1.3 [Numerical Analysis]: Numerical Linear Algebralinear systems (direct and
Algorithms for Nonnegative Matrix Factorization
 In NIPS
, 2001
"... Nonnegative matrix factorization (NMF) has previously been shown to be a useful decomposition for multivariate data. Two different multiplicative algorithms for NMF are analyzed. They differ only slightly in the multiplicative factor used in the update rules. One algorithm can be shown to minim ..."
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Cited by 1230 (5 self)
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to minimize the conventional least squares error while the other minimizes the generalized KullbackLeibler divergence. The monotonic convergence of both algorithms can be proven using an auxiliary function analogous to that used for proving convergence of the ExpectationMaximization algorithm
Results 1  10
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382,644