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@book{Facchinei2003,
address = {New York},
author = {Francisco Facchinei and Jong-Shi Pang},
isbn = {978-0-387-21814-4},
publisher = {Springer},
title = {{Finite-dimensional variational inequalities and complementarity problems}},
year = {2003}
}
@article{Munson2001,
abstract = {Complementarity solvers are continually being challenged by modelers demanding improved reliability and scalability. Building upon a strong theoretical background, the semismooth algorithm has the potential to meet both of these requirements. We discuss relevant theory associated with the algorithm and then describe a sophisticated implementation in detail. Particular emphasis is given to the use of preconditioned iterative methods to solve the (nonsymmetric) systems of linear equations generated at each iteration and robust methods for dealing with singularity. Results on the MCPLIB test suite indicate that the code is reliable and efficient and scales well to very large problems.},
author = {Todd S. Munson and Francisco Facchinei and Michael C. Ferris and Andreas Fischer and Christian Kanzow},
doi = {10.1287/ijoc.13.4.294.9734},
eprint = {http://pubsonline.informs.org/doi/pdf/10.1287/ijoc.13.4.294.9734},
journal = {INFORMS Journal on Computing},
localfile = {mathematic/Munson2001.pdf},
number = {4},
pages = {294--311},
title = {{The Semismooth Algorithm for Large Scale Complementarity Problems}},
url = {http://pubsonline.informs.org/doi/abs/10.1287/ijoc.13.4.294.9734},
volume = {13},
year = {2001}
}
@article{Chen2000,
abstract = {We introduce a new NCP-function in order to reformulate the nonlinear complementarity problem as a nonsmooth system of equations. This new NCP-function turns out to have stronger theoretical properties than the widely used Fischer-Burmeister function and other NCP-functions suggested previously. Moreover, numerical experience indicates that a semismooth Newton method based on this new NCP-function performs considerably better than the corresponding method based on the Fischer-Burmeister function.},
author = {Bintong Chen and Xiaojun Chen and Christian Kanzow},
doi = {10.1007/PL00011375},
issn = {0025-5610},
journal = {Mathematical Programming},
keywords = {Key words: nonlinear complementarity problem -- Newton{\rq}s method -- semismoothness},
language = {English},
localfile = {mathematic/Chen2000.pdf},
number = {1},
pages = {211--216},
publisher = {Springer-Verlag},
title = {{A penalized Fischer-Burmeister NCP-function}},
url = {http://dx.doi.org/10.1007/PL00011375},
volume = {88},
year = {2000}
}
@misc{Chen1997a,
author = {Bintong Chen and Xiaojun Chen and Christian Kanzow and B. Chen and X. Chen and C. Kanzow},
localfile = {mathematic/Chen1997.pdf},
title = {{A Penalized Fischer-Burmeister Ncp-Function: Theoretical Investigation And Numerical Results}},
url = {http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.51.209},
year = {1997}
}
@book{Dennis1983,
author = {J.E. Dennis and R.B. Schnabel},
isbn = {9780136272168},
lccn = {82023478},
publisher = {Prentice-Hall},
title = {{Numerical methods for unconstrained optimization and nonlinear equations}},
year = {1983}
}
@article{Cline1979,
abstract = {It is important in practice when solving linear systems to have an economical method for estimating the condition number κ(A) of the matrix of coefficients. An algorithm involving O(n2) arithmetic operations is described; it gives a reliable indication of the order of magnitude of κ(A).},
author = {A. K. Cline and C. B. Moler and G. W. Stewart and J. H. Wilkinson},
journal = {SIAM Journal on Numerical Analysis},
localfile = {mathematic/Cline1979.pdf},
month = {April},
number = {2},
pages = {368--375},
publisher = {SIAM Journal on Numerical Analysis},
title = {{An Estimate for the Condition Number of a Matrix}},
url = {http://www.jstor.org/stable/view/2156842},
volume = {16},
year = {1979}
}
@article{Hager1984,
abstract = {A new technique for estimating the 11 condition number of a matrix is developed and compared to an earlier scheme.},
author = {William W. Hager},
journal = {SIAM Journal on Scientific and statistical Computing},
keywords = {Condition number},
localfile = {mathematic/Hager1984.pdf},
month = {June},
number = {2},
pages = {311--316},
publisher = {Society for Industrial and Applied Mathematics},
title = {{Condition estimates}},
volume = {5},
year = {1984}
}
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