The Semismooth Algorithm for Large Scale Complementarity Problems

References

  • Billups S. C.Algorithms for complementarity problems and generalized equations (1995) (Computer Sciences Department, University of Wisconsin-Madison, Madison, WI) . Ph.D.thesisGoogle Scholar
  • Brooke A., Kendrick D., Meeraus A.GAMS: A User's Guide (1988) (The Scientific Press, South San Francisco, CA) Google Scholar
  • Chen B., Chen X., Kanzow C. A penalized Fischer-Burmeister NCP-function: Theoretical investigation and numerical results. Mathematical Programming (2000) 88:211–216CrossrefGoogle Scholar
  • Clarke F. H.Optimization and Nonsmooth Analysis (1983) (John Wiley & Sons, New York) Google Scholar
  • De Luca T., Facchinei F., Kanzow C. A semismooth equation approach to the solution of nonlinear complementarity problems. Mathematical Programming (1996) 75:407–439CrossrefGoogle Scholar
  • De Luca T., Facchinei F., Kanzow C. A theoretical and numerical comparison of some semismooth algorithms for complementarity problems. Computational Optimization and Applications (2000) 16:173–205CrossrefGoogle Scholar
  • Dirkse S. P., Ferris M. C. MCPLIB: a collection of nonlinear mixed complementarity problems. Optimization Methods and Software (1995a) 5:319–345CrossrefGoogle Scholar
  • Dirkse S. P., Ferris M. C. The PATH solver: a non-monotone stabilization scheme for mixed complementarity problems. Optimization Methods and Software (1995b) 5:123–156CrossrefGoogle Scholar
  • Facchinei F., Fischer A., Kanzow C., Ferris M. C., Pang J. S. A semismooth Newton method for variational inequalities: The case of box constraints. Complementarity and Variational Problems: State of the Art (1997) (SIAM Publications, Philadelphia, PA) 76–90Google Scholar
  • Ferris M. C., Fourer R., Gay D. M. Expressing complementarity problems and communicating them to solvers. SIAM Journal on Optimization (1999a) 9:991–1009CrossrefGoogle Scholar
  • Ferris M. C., Kanzow C., Munson T. S. Feasible descent algorithms for mixed complementarity problems. Mathematical Programming (1999b) 86:475–497CrossrefGoogle Scholar
  • Ferris M. C., Lucidi S. Nonmonotone stabilization methods for nonlinear equations. Journal of Optimization Theory and Applications (1994) 81:53–71CrossrefGoogle Scholar
  • Ferris M. C., Mesnier M. P., Moré J. NEOS and Condor: solving nonlinear optimization problems over the internet. ACM Transactions on Mathematical Software (2000) 26:1–18CrossrefGoogle Scholar
  • Ferris M. C., Munson T. S. Interfaces to PATH 3.0: design, implementation and usage. Computational Optimization and Applications (1999) 12:207–227CrossrefGoogle Scholar
  • Ferris M. C., Munson T. S. Complementarity problems in GAMS and the PATH solver. Journal of Economic Dynamics and Control (2000) 24:165–188CrossrefGoogle Scholar
  • Ferris M. C., Pang J. S.Complementarity and Variational Problems: State of the Art (1997a) (SIAM Publications, Philadelphia, PA) Google Scholar
  • Ferris M. C., Pang J. S. Engineering and economic applications of complementarity problems. SIAM Review (1997b) 39:669–713CrossrefGoogle Scholar
  • Fischer A. A special Newton-type optimization method. Optimization (1992) 24:269–284CrossrefGoogle Scholar
  • Fourer R., Gay D. M., Kernighan B. W.AMPL: A Modeling Language for Mathematical Programming (1993) (Duxbury Press, Pacific Grove, CA) Google Scholar
  • Gill P. E., Murray W., Saunders M. A., Wright M. H. Maintaining LU factors of a general sparse matrix. Linear Algebra and Its Applications (1987) 88/89:239–270CrossrefGoogle Scholar
  • Golub G. H., Kahan W. Calculating the singular values and pseudoinverse of a matrix. SIAM Journal on Numerical Analysis (1965) 2:205–224Google Scholar
  • Grippo L., Lampariello F., Lucidi S. A nonmonotone line search technique for Newton's method. SIAM Journal on Numerical Analysis (1986) 23:707–716CrossrefGoogle Scholar
  • Grippo L., Lampariello F., Lucidi S. A class of non-monotone stabilization methods in unconstrained optimization. Numerische Mathematik (1991) 59:779–805CrossrefGoogle Scholar
  • Harrison G. W., Rutherford T. F., Tarr D. Quantifying the Uruguay round. The Economic Journal (1997) 107:1405–1430CrossrefGoogle Scholar
  • Josephy N. H.Newton's method for generalized equations (1979) (Mathematics Research Center, University of Wisconsin, Madison, WI) . Technical Summary Report 1965Google Scholar
  • Lemke C. E. Bimatrix equilibrium points and mathematical programming. Management Science (1965) 11:681–689LinkGoogle Scholar
  • Manne A. S., Rutherford T. F. International trade in oil, gas and carbon emission rights: An intertemporal general equilibrium model. The Energy Journal (1993) 14:1–20Google Scholar
  • Mathiesen L. Computation of economic equilibria by a sequence of linear complementarity problems. Mathematical Programming Study (1985) 23:144–162CrossrefGoogle Scholar
  • MATLABUser's Guide (2000) (The MathWorks, Inc., Natick, MA) Google Scholar
  • Mifflin R. Semismooth and semiconvex functions in constrained optimization. SIAM Journal on Control and Optimization (1977) 15:957–972CrossrefGoogle Scholar
  • Murtagh B. A., Saunders M. A.MINOS 5.0 user's guide (1983) (Stanford University, Stanford, CA) . Technical Report SOL 83.20Google Scholar
  • Paige C. C., Saunders M. A. LSQR: An algorithm for sparse linear equations and sparse least squares. ACM Transactions on Mathematical Software (1982) 8:43–71CrossrefGoogle Scholar
  • Qi L. Convergence analysis of some algorithms for solving nonsmooth equations. Mathematics of Operations Research (1993) 18:227–244LinkGoogle Scholar
  • Qi L., Sun J. A nonsmooth version of Newton's method. Mathematical Programming (1993) 58:353–368CrossrefGoogle Scholar
  • Robinson S. M. Strongly regular generalized equations. Mathematics of Operations Research (1980) 5:43–62LinkGoogle Scholar
  • Robinson S. M. Normal maps induced by linear transformations. Mathematics of Operations Research (1992) 17:691–714LinkGoogle Scholar
  • Rutherford T. F.MILES: A mixed inequality and nonlinear equation solver (1993) (Department of Economics, University of Colorado, Boulder, CO) . Working PaperGoogle Scholar
  • Rutherford T. F. Extensions of GAMS for complementarity problems arising in applied economic analysis. Journal of Economic Dynamics and Control (1995) 19:1299–1324CrossrefGoogle Scholar
  • Saad Y.Iterative Methods for Sparse Linear Systems (1996) (PWS Publishing Company, Boston, MA) Google Scholar
  • Tin-Loi F., Ferris M. C., Karihaloo B. L., Mai Y. W., Ripley M. I., Ritchie R. O. Holonomic analysis of quasibrittle fracture with nonlinear softening. Advances in Fracture Research (1997) 2(Pergamon Press, Oxford, UK) 2183–2190Google Scholar
  • Vanderbei R. J.Linear Programming: Foundations and Extensions (1997) (Kluwer Academic Publishers, Boston, MA) Google Scholar
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