An almost smooth equation reformulation to the nonlinear complementarity problem and Newton's method

References

• Chen , X. 2000 . Smoothing methods for complementarity problems and the application: a survey . J. Oper. Res. , 43 ( 1 ) : 32 – 47 .
   Web of Science ®Google Scholar
• Chen , J. S. 2006 . The semismooth-related properties of a merit function and a descent method for the nonlinear complementarity problem . J. Global Optim. , 36 : 565 – 580 .
   Web of Science ®Google Scholar
• Chen , J. S. 2007 . On some NCP-functions based on the generalized Fischer–Buemeister function . Asia-Pacific J. Oper. Res. , 24 : 401 – 420 .
   Web of Science ®Google Scholar
• Chen , J. S. and Pan , S. 2008 . A family of NCP functions and a descent method for the nonlinear complementarity problem . Comput. Optim. Appl. , 40 : 389 – 404 .
   Web of Science ®Google Scholar
• Chen , X. , Qi , L. and Sun , D. 1998 . Global and superlinear convergence of the smoothing Newton method and its application to general box constrained inequality . Math. Comput. , 67 ( 222 ) : 519 – 540 .
   Web of Science ®Google Scholar
• Chen , B. , Chen , X. and Kanzow , C. 2000 . A penalized Fischer–Burmeister NCP-function . Math. Program. Ser. , A 88 : 211 – 216 .
   Web of Science ®Google Scholar
• Chen , X. , Qi , L. and Yang , Y. F. 2002 . Lagrangian globalization methods for nonlinear complementarity problems . J. Optim. Theory Appl. , 112 ( 1 ) : 77 – 95 .
   Web of Science ®Google Scholar
• De Luca , T. , Facchinei , F. and Kanzow , C. 1996 . A semismooth equation approach to the solution of nonlinear complementarity problems . Math. Program , 75 : 407 – 439 .
   Web of Science ®Google Scholar
• Facchinei , F. and Soares , J. 1994 . “ Testing a new class of algorithms for nonlinear complementarity problems ” . In Technical Report, Dipartmento di Informatica e Sistemistica, Universita di Roma La Sapienza Rome , , Italy
   Google Scholar
• Facchinei , F. and Soares , J. 1997 . A new merit function for nonlinear complementarity problems and a related algorithm . SIAM J. Optim. , 7 : 225 – 247 .
   Web of Science ®Google Scholar
• Facchinei , F. , Fischer , A. and Kanzow , C. 1996 . “ Inexact Newton methods for semismooth equations with applications to variational inequality problems ” . In Nonlinear Optimization and Applications , Edited by: Pillo , G. Di. and Giannessi , F. 125 – 139 . New York : Plenum Press .
   Google Scholar
• Fischer , A. 1998 . New constrained optimization reformulation of complementarity problems . J. Optim. Theory Appl. , 97 ( 1 ) : 105 – 117 .
   Web of Science ®Google Scholar
• Fischer , A. and Jiang , H. Y. 2000 . Merit functions for complementarity and related problems: a survey . Comput. Optim. Appl. , 17 : 159 – 182 .
   Web of Science ®Google Scholar
• Fukushima , M. 1992 . Equivalent differentiable optimization problems and descent methods for asymmetric variational inequality problems . Math. Program , 58 : 99 – 110 .
   Web of Science ®Google Scholar
• Fukushima , M. 1996 . “ Merit functions for variational inequality and complementarity problems ” . In Nonlinear Optimization and Applications , Edited by: Pillo , G. Di. and Giannessi , F. 155 – 170 . New York : Plenum Press .
   Google Scholar
• Geiger , C. and Kanzow , C. 1996 . On the resolution of monotone complementarity problems . Comput. Optim. Appl. , 5 : 155 – 173 .
   Google Scholar
• Hallman , W. P. and Kaneko , I. 1979 . On the connectedness of the set of almost complementary paths of a linear complementarity problem . Math. Program , 16 : 384 – 385 .
   Web of Science ®Google Scholar
• Hock , W. and Schitkkowski , K. 1981 . “ Test examples for nonlinear programming codes ” . In lecture notes in economics and mathematical systems , Vol. 187 , Berlin : Springer .
   Google Scholar
• Jiang , H. and Qi , L. 1997 . A new nonsmooth equations approach to nonlinear complementarity problems . SIAM J. Control Optim. , 35 ( 1 ) : 178 – 193 .
   Web of Science ®Google Scholar
• Kanzow , C. 1994 . Some equation-based methods for the nonlinear complementarity problem . Optim. Meth. Softw. , 3 : 139 – 155 .
   Google Scholar
• Kanzow , C. 1996 . Nonlinear complementarity as unconstrained optimization . J. Optim. Theory Appl. , 88 : 139 – 155 .
   Web of Science ®Google Scholar
• Kanzow , C. 1996 . Some noninterior continuation methods for linear complementarity problems . SIAM J. Matrix Anal. Appl. , 17 : 851 – 868 .
   Web of Science ®Google Scholar
• Kanzow , C. and Kleinmichel , H. 1998 . A new class of semismooth Newton-type methods for nonlinear complementarity problems . Comput. Optim. Appl. , 11 : 227 – 251 .
   Web of Science ®Google Scholar
• Li , C. L. , Zeng , J. P. and Zhou , S. Z. 2004 . Convergence analysis of generalized Schwarz algorithms for solving obstacle problems with T-monotone operator . Comput. Math. Appl. , 48 : 373 – 386 .
   Web of Science ®Google Scholar
• Lukšan , L. 1994 . Inexact trust region method of large sparse systems of nonlinear equations . J. Optim. Theory Appl. , 81 : 569 – 590 .
   Web of Science ®Google Scholar
• Mathiesen , L. 1987 . An algorithm based on a sequence of linear complementarity problems applied to a walrasian equilibrium model: an example . Math. Program , 37 : 1 – 18 .
   Web of Science ®Google Scholar
• Mangasarian , O. L. and Solodov , M. V. 1993 . Nonlinear complementarity as unconstrained and constrained minimization . Math. Program , 62 : 277 – 297 .
   Web of Science ®Google Scholar
• Mifflin , R. 1977 . Semismooth and semiconvex functions in constrained optimization . SIAM J. Control Optim. , 15 : 957 – 972 .
   Web of Science ®Google Scholar
• Murty , K. G. and Yu , V. F. “ Linear Complentarity, Linear and Nonlinear Programming ” . Internet Edition
   Google Scholar
• Pang , J.-S. 1986 . Inexact Newton method for the nonlinear complementarity problem . Math. Program , 36 : 54 – 71 .
   Web of Science ®Google Scholar
• Qi , L. 1993 . Convergence analysis of some algorithms for solving nonsmooth equations . Math. Oper. Res. , 18 ( 1 ) : 227 – 244 .
   Web of Science ®Google Scholar
• Qi , L. and Sun , J. 1993 . A nonsmooth version of Newton's method . Math. Program. , 58 : 353 – 367 .
   Web of Science ®Google Scholar
• Qi , L. and Sun , D. 2002 . Smoothing functions and smoothing Newton-methods for complementarity and variational inequality problems . J. Optim. Theory Appl. , 113 ( 1 ) : 121 – 147 .
   Web of Science ®Google Scholar
• Qi , L. and Tseng , P. 2007 . On almost smooth functions and piecewise smooth functions . Nonlinear Anal. , 67 : 773 – 794 .
   Web of Science ®Google Scholar
• Qi , L. and Yang , Y. F. 2002 . NCP-functions applied to Lagrangian globalization for the nonlinear complementarity problem . J. Global Optim. , 24 : 261 – 283 .
   Web of Science ®Google Scholar
• Qi , L. , Sun , D. and Zhou , G. L. 2000 . A new look at smoothing Newton methods for nonlinear complementarity problems and box constrained variational inequalities . Math. Program. , 87 : 1 – 35 .
   Web of Science ®Google Scholar
• Sun , D. and Qi , L. 1999 . On NCP-Functions . Comput. Optim. Appl. , 13 : 201 – 220 .
   Web of Science ®Google Scholar
• Tarvainen , P. 1999 . Two-level Schwarz method for unilateral variational inequalities . IMA J. Numer. Anal. , 19 : 273 – 290 .
   Web of Science ®Google Scholar
• Tseng , P. 1996 . Growth behavior of a class of merit functions for nonlinear complementarity problem . J. Optim. Theory Appl. , 89 : 17 – 37 .
   Web of Science ®Google Scholar
• Watson , L. J. 1979 . Solving the nonlinear complementarity problem by a homotopy method . SIAM J. Control Optim. , 17 : 36 – 46 .
   Web of Science ®Google Scholar