@book{Dennis, author = "J. E. Dennis and R. B. Schnabel", title = "Numerical methods for unconstrained optimization and nonlinear equations", year = "1983", publisher = "Prentice-Hall" } @article{Gabriel, author = "S. A. Gabriel and J-S Pang", title = "An inexact {NE/SQP} method for solving the nonlinear complementarity problem", Journal = "Computational Optimization and Computations", volume = "1", year = "1992", page = "67--91" } @article{Zhang2, author = "Y. Zhang and R. A. Tapia", title = "A superlinearly convergent polynomial primal-dual interior-point algorithm for linear programming", Journal = "SIAM J. Optimization", volume = "3", year = "1993", page = "118--133" } @techreport{Tapia, author = "A. S. El-Bakry and R. A. Tapia and T. Tsuchiya and Y. Zhang", title = "On the formulation and theory of the primal-dual {N}ewton interior-point method for nonlinear programming", type="{Technical Report TR92-40}", institution="{Department of Computational and Applied Mathematics, Rice University}", year = "1992", } @techreport{Simantiraki, author = "E. Simantiraki and D.F. Shanno", title = "An infeasible-interior-point algorithm for linear complementarity problems", type="{Rutcor Research Report 7-95}", institution="{RUTCOR, and Graduate School of Management, Rutgers University}", year = "1995", } @techreport{More, author = "J.J. Mor\'e", title = "Global methods for nonlinear complementarity problems", type = "{Preprint MCS-P429-0494}", year = "1994", institution = "Argonne National Laboratory, Mathematics and Computer Science Division", address = "Argonne, Illinois" } @techreport{Dirkse, author = "S.P. Dirkse", title = "Robust solutions of mixed complementarity problems", type = "{Ph.D. Thesis}", year = "1994", institution = "Computer Science Department, University of Wisconsin", address = "Madison, Wisconsin" } @techreport{MCPLIB, author = "S. Dirkse and M. Ferris", title = "{MCPLIB}: A collection of nonlinear mixed complementarity problems", type = "{Technical Report}", year = "1994", institution = "Computer Science Department, University of Wisconsin", address = "Madison, Wisconsin" } @article{Hansen, author = "T. Hansen and T.C. Koopmans", title = "On the definition and computation of a capital stock invariant under optimization", journal = "Journal of Economic Theory", volume = "5", year = "1972", pages = "487--523" } @article{HarkXiao, author = "P.T. Harker and B. Xiao", title = "Newton's method for the nonlinear complementarity problem: a {B}-differentiable equation approach", journal = "Mathematical Programming", volume = "48", year = "1990", pages = "339--357" } @article{HarkPang, author = "P.T. Harker and J-S. Pang", title = "Finite-dimensional variational inequality and nonlinear complementarity problems: a survey of theory, algorithms and applications", journal = "Mathematical Programming", volume = "{\it B} 48", year = "1990", pages = "161--220" } @article{Monteiro, author = "R.D.C. Monteiro and J.S. Pang and T. Wang", title = "A positive algorithm for the nonlinear complementarity problem", journal = "SIAM J. Optimization", volume = "5", year = "1995", pages = "129--148" } @techreport{Wang, author = "T. Wang and R.D.C. Monteiro and J.S. Pang", title = "An Interior point potential reduction method for constrained equations", institution = "Department of Mathematical Sciences, The Johns Hopkins University", year = "1994", } @article{Hoppe, author = "R.H.W. Hoppe and H.D. Mittelmann", title = "A multi-grid continuation strategy for parameter-dependent variational inequalities", journal = "Journal of Computational and Applied Mathematics", volume = "26", year = "1989", pages = "35--46" } @article{Kostreva, author = "M.M Kostreva", title = "Elasto-hydrodynamic lubrication: a nonlinear complementarity problem", journal = "International Journal for Numerical Methods in Fluids", volume = "4", year = "1984", pages = "377--397" } @article{Miersemann, author = "E. Miersemann and H. Mittelmann", title = "Continuation for parameterized nonlinear variational inequalities", journal = "Journal of Computational and Applied Mathematics", volume = "26", year = "1989", pages = "23--34" } @book{Schit, author = "W. Hock and K. Schittkowski", title = "Test Examples for Nonlinear Programming Codes", volume = "187", series = "Lecture Notes in Economics and Mathematical Systems", year = "1981", publisher = "Springer Verlag", address = "Berlin, Germany" } @article{Tobin, author = "R.L. Tobin", title = "Variable dimension spatial price equilibrium algorithm", journal = "Mathematical Programming", volume = "40", year = "1988", pages = "33--51" } @article{Hogan, author = "W.W. Hogan", title = "Energy policy models for project independence", journal = "Computers and Operations Research", volume = "2", year = "1975", pages = "251--271" } @techreport{PIES, author = "N.H Josephy", title = "A Newton method for the PIES energy model", type = "{Technical Summary Report \#1971}", year = "1979", institution = "Mathematics Research Center, University of Wisconsin", address = "Madison, Wisconsin" } @techreport{Josephy, author = "N.H Josephy", title = "Newton's method for generalized equations", type = "{Technical Summary Report \#1965}", year = "1979", institution = "Mathematics Research Center, University of Wisconsin", address = "Madison, Wisconsin" } @article{Path, author = "S. Dirkse and M. Ferris", title = "The PATH solver: A non-monotone stabilization scheme for mixed complementarity problems", journal = "Optimization Methods \& Software", year = "1994 To appear", } @article{Koji, author = "M. Kojima and S. Shindo", title = "Extensions of Newton and quasi-Newton methods to systems of ${PC}^1$ equations", journal = "Journal of Operations Research Society of Japan", volume = "29", year = "1986", pages = "352--374" } @article{Mathiesen, author = "L. Mathiesen", title = "An algorithm based on a sequence of linear complementarity problems applied to a Walsarian equilibrium model: an example", journal = "Mathematical Programming", volume = "37", year = "1987", pages = "1--18" } @article{Murphy, author = "F.H. Murphy and H.D. Sherali and A.L. Soyster", title = "A mathematical programming approach for determining oligopolistic market equilibrium", journal = "Mathematical Programming", volume = "24", year = "1982", pages = "92--106" } @article{Pang, author = "J.S. Pang and S. A. Gabriel", title = "{NE/SQP}: A robust algorithm for the nonlinear complementarity problem", journal = "Mathematical Programming", volume = "60", year = "1993", pages = "295--337" } @book{Scarf, author = "H. Scarf", title = "The Computation of Economic Equilibria", year = "1973", publisher = "Yale University Press", address = "New Haven, CT" } @techreport{Xiao, author = "B. Xiao", title = "Global Newton methods for nonlinear problems and variational inequalities: a {B}-differentiable equation approach ", type = "{Ph.D. Thesis}", year = "1990", institution = "Department of Decision Sciences, The Warton School, University of Pennsylvania", address = "Philadelphia, PA" } @techreport{Umfpack, author = "T. A. Davis", title = "Users' guide for the unsymmetric-pattern multifrontal Package ({UMFPACK})", type = "{Technical Report}", year = "1993", institution = "Computer and Information Sciences Department, University of Florida", address = "Gainesville, Florida" }