On a class of quasi-variational inequalities

In this paper we give an existence result for a class of quasi-variational inequalities. Further, we propose a nonsmooth variant of the Newton method for their numerical solution. Using the tools of sensitivity and stability theory and nonsmooth analysis, criteria are formulated ensuring the local superlinear convergence. The method is applied to the discretized contact problem with the Coulomb friction model

[1]  R. Mifflin.  Semismooth and Semiconvex Functions in Constrained Optimization , 1977 .

[2]  Patrick T. Harker,et al.  Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications , 1990, Math. Program..

[3]  Stephen M. Robinson,et al.  An Implicit-Function Theorem for a Class of Nonsmooth Functions , 1991, Math. Oper. Res..

[4]  U. Mosco.  Implicit variational problems and quasi variational inequalities , 1976 .

[5]  T. Ichiishi.  Game theory for economic analysis , 1983 .

[6]  J. Pang.  THE IMPLICIT COMPLEMENTARITY PROBLEM , 1981 .

[7]  Jaroslav Haslinger,et al.  The reciprocal variational approach to the Signorini problem with friction. Approximation results , 1984, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[8]  Stephen M. Robinson,et al.  Strongly Regular Generalized Equations , 1980, Math. Oper. Res..

[9]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[10]  Jerzy Kyparisis,et al.  Solution behavior for parametric implicit complementarity problems , 1992, Math. Program..

[11]  Liqun Qi,et al.  A nonsmooth version of Newton's method , 1993, Math. Program..

[12]  F. Clarke.  Optimization And Nonsmooth Analysis , 1983 .

[13]  B. Bank,et al.  Non-Linear Parametric Optimization , 1983 .

[14]  Liqun Qi,et al.  Convergence Analysis of Some Algorithms for Solving Nonsmooth Equations , 1993, Math. Oper. Res..

[15]  P. Harker.  Generalized Nash games and quasi-variational inequalities , 1991 .

[16]  J. Jarusek.  Contact problems with bounded friction. Coercive case , 1983 .

[17]  Jirí V. Outrata,et al.  A Newton method for a class of quasi-variational inequalities , 1995, Comput. Optim. Appl..

[18]  A. Bensoussan,et al.  Contrôle impulsionnel et inéquations quasi variationnelles , 1982 .

[19]  Jirí V. Outrata,et al.  On Optimization Problems with Variational Inequality Constraints , 1994, SIAM J. Optim..

[20]  J. S. Pang,et al.  The Generalized Quasi-Variational Inequality Problem , 1982, Math. Oper. Res..

[21]  E. Peterson,et al.  Generalized variational inequalities , 1982 .

[22]  C. Baiocchi,et al.  Variational and quasivariational inequalities: Applications to free boundary problems , 1983 .

[23]  Yaguang Yang.  A new approach to uncertain parameter linear programming , 1991 .

[24]  J. Haslinger,et al.  Solution of Variational Inequalities in Mechanics , 1988 .

[25]  Jerzy Kyparisis.  Solution differentiability for variational inequalities , 1990, Math. Program..