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345,133
On the Asymmetric Eigenvalue Complementarity Problem
, 2009
"... In this paper, we discuss the Eigenvalue Complementarity Problem (EiCP) where at least one of its defining matrices is asymmetric. A sufficient condition for the existence of a solution to the EiCP is established. The EiCP is shown to be equivalent to finding a global minimum of an appropriate merit ..."
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Cited by 3 (1 self)
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In this paper, we discuss the Eigenvalue Complementarity Problem (EiCP) where at least one of its defining matrices is asymmetric. A sufficient condition for the existence of a solution to the EiCP is established. The EiCP is shown to be equivalent to finding a global minimum of an appropriate
On the Solution of the Symmetric Eigenvalue Complementarity Problem by the . . .
, 2008
"... This paper is devoted to the Eigenvalue Complementarity Problem (EiCP) with symmetric real matrices. This problem is equivalent to finding a stationary point of a differentiable optimization program involving the Rayleigh quotient on a simplex [22]. We discuss a logarithmic function and a quadratic ..."
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Cited by 16 (6 self)
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This paper is devoted to the Eigenvalue Complementarity Problem (EiCP) with symmetric real matrices. This problem is equivalent to finding a stationary point of a differentiable optimization program involving the Rayleigh quotient on a simplex [22]. We discuss a logarithmic function and a
Research Article LevenbergMarquardt Method for the Eigenvalue Complementarity Problem
"... License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The eigenvalue complementarity problem (EiCP) is a kind of very useful model, which is widely used in the study ofmany problems in mechanics, engineering, and economic ..."
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License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The eigenvalue complementarity problem (EiCP) is a kind of very useful model, which is widely used in the study ofmany problems in mechanics, engineering
DOI 10.1007/s1058900790170 The eigenvalue complementarity problem
, 2007
"... Abstract In this paper an eigenvalue complementarity problem (EiCP) is studied, which finds its origins in the solution of a contact problem in mechanics. The EiCP is shown to be equivalent to a Nonlinear Complementarity Problem, a Mathematical Programming Problem with Complementarity Constraints an ..."
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Abstract In this paper an eigenvalue complementarity problem (EiCP) is studied, which finds its origins in the solution of a contact problem in mechanics. The EiCP is shown to be equivalent to a Nonlinear Complementarity Problem, a Mathematical Programming Problem with Complementarity Constraints
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 762 (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
Nonlinear component analysis as a kernel eigenvalue problem

, 1996
"... We describe a new method for performing a nonlinear form of Principal Component Analysis. By the use of integral operator kernel functions, we can efficiently compute principal components in highdimensional feature spaces, related to input space by some nonlinear map; for instance the space of all ..."
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Cited by 1549 (83 self)
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We describe a new method for performing a nonlinear form of Principal Component Analysis. By the use of integral operator kernel functions, we can efficiently compute principal components in highdimensional feature spaces, related to input space by some nonlinear map; for instance the space of all possible 5pixel products in 16x16 images. We give the derivation of the method, along with a discussion of other techniques which can be made nonlinear with the kernel approach; and present first experimental results on nonlinear feature extraction for pattern recognition.
An iterative method for the solution of the eigenvalue problem of linear differential and integral
, 1950
"... The present investigation designs a systematic method for finding the latent roots and the principal axes of a matrix, without reducing the order of the matrix. It is characterized by a wide field of applicability and great accuracy, since the accumulation of rounding errors is avoided, through the ..."
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Cited by 528 (0 self)
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the process of "minimized iterations". Moreover, the method leads to a well convergent successive approximation procedure by which the solution of integral equations of the Fredholm type and the solution of the eigenvalue problem of linear differential and integral operators may be accomplished. I.
ORIGINAL PAPER
, 2008
"... On the solution of the symmetric eigenvalue complementarity problem by the spectral projected gradient algorithm ..."
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On the solution of the symmetric eigenvalue complementarity problem by the spectral projected gradient algorithm
Improved Approximation Algorithms for Maximum Cut and Satisfiability Problems Using Semidefinite Programming
 Journal of the ACM
, 1995
"... We present randomized approximation algorithms for the maximum cut (MAX CUT) and maximum 2satisfiability (MAX 2SAT) problems that always deliver solutions of expected value at least .87856 times the optimal value. These algorithms use a simple and elegant technique that randomly rounds the solution ..."
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Cited by 1200 (13 self)
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the solution to a nonlinear programming relaxation. This relaxation can be interpreted both as a semidefinite program and as an eigenvalue minimization problem. The best previously known approximation algorithms for these problems had performance guarantees of ...
Consensus Problems in Networks of Agents with Switching Topology and TimeDelays
, 2003
"... In this paper, we discuss consensus problems for a network of dynamic agents with fixed and switching topologies. We analyze three cases: i) networks with switching topology and no timedelays, ii) networks with fixed topology and communication timedelays, and iii) maxconsensus problems (or leader ..."
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Cited by 1053 (18 self)
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In this paper, we discuss consensus problems for a network of dynamic agents with fixed and switching topologies. We analyze three cases: i) networks with switching topology and no timedelays, ii) networks with fixed topology and communication timedelays, and iii) maxconsensus problems (or
Results 1  10
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345,133