Well-posedness of Hemivariational Inequalities and Inclusion Problems

In the present paper, we generalize the concept of well-posedness to a hemivariational inequality, give some metric characterizations of the wellposed hemivariational inequality, and derive some conditions under which the hemivariational inequality is strongly well-posed in the generalized sense. Also, we show that the well-posedness of the hemivariational inequality is equivalent to the well-posedness of the corresponding inclusion problem.

[1]  Jen-Chih Yao,et al.  Iterated function systems and well-posedness , 2009 .

[2]  Rong Hu,et al.  Parametric well-posedness for variational inequalities defined by bifunctions , 2007, Comput. Math. Appl..

[3]  B. Lemaire,et al.  WELL-POSEDNESS, CONDITIONING AND REGULARIZATION OF MINIMIZATION, INCLUSION AND FIXED-POINT PROBLEMS , 2013 .

[4]  Kok Lay Teo,et al.  Some Remarks on the Minty Vector Variational Inequality , 2004 .

[5]  Yi-bin Xiao,et al.  Sub–supersolution method and extremal solutions for higher order quasi-linear elliptic hemi-variational inequalities☆ , 2007 .

[6]  Dumitru Motreanu,et al.  Minimax Theorems and Qualitative Properties of the Solutions of Hemivariational Inequalities , 1998 .

[7]  E. Zeidler.  Nonlinear functional analysis and its applications , 1988 .

[8]  J. Revalski,et al.  Recent developments in well-posed variational problems , 1995 .

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

[10]  Fioravante Patrone,et al.  On the Tikhonov Well-Posedness of Concave Games and Cournot Oligopoly Games , 2002 .

[11]  Jen-Chih Yao,et al.  EXISTENCE THEOREMS FOR GENERALIZED VECTOR VARIATIONAL INEQUALITIES WITH PSEUDOMONOTONICITY AND THEIR APPLICATIONS , 2008 .

[12]  Kenji Kimura,et al.  WELL-POSEDNESS FOR PARAMETRIC VECTOR EQUILIBRIUM PROBLEMS WITH APPLICATIONS , 2008 .

[13]  Chong Li,et al.  Well-posedness of a class of perturbed optimization problems in Banach spaces ✩ , 2008 .

[14]  R. Lucchetti,et al.  well posed saddle point problems , 2005 .

[15]  Jen-Chih Yao,et al.  Well-posedness of mixed variational inequalities, inclusion problems and fixed point problems , 2008, J. Glob. Optim..

[16]  W. Marsden.  I and J , 2012 .

[17]  Anna Ochal,et al.  Dynamic bilateral contact problem for viscoelastic piezoelectric materials with adhesion , 2008 .

[18]  P. D. Panagiotopoulos,et al.  Nonconvex energy functions. Hemivariational inequalities and substationarity principles , 1983 .

[19]  Jen-Chih Yao,et al.  Well-posedness by perturbations of mixed variational inequalities in Banach spaces , 2010, Eur. J. Oper. Res..

[20]  T. Zolezzi,et al.  Well-Posed Optimization Problems , 1993 .

[21]  Panagiotis D. Panagiotopoulos,et al.  Hemivariational Inequalities: Applications in Mechanics and Engineering , 1993 .

[22]  Matteo Rocca,et al.  Well Posedness in Vector Optimization Problems and Vector Variational Inequalities , 2007 .

[23]  Existence and comparison results for variational-hemivariational inequalities , 2005 .

[24]  Jen-Chih Yao,et al.  Well-posedness of generalized mixed variational inequalities, inclusion problems and fixed-point problems , 2008 .

[25]  Jen-Chih Yao,et al.  Solution Methods for Pseudomonotone Variational Inequalities , 2008 .

[26]  Jen-Chih Yao,et al.  WELL-POSEDNESS FOR VECTOR QUASIEQUILIBRIA , 2009 .

[27]  Nan-Jing Huang,et al.  Browder-Tikhonov regularization for a class of evolution second order hemivariational inequalities , 2009, J. Glob. Optim..

[28]  Zhenhai Liu,et al.  Existence results for quasilinear parabolic hemivariational inequalities , 2008 .

[29]  Jen-Chih Yao,et al.  Well-Posedness for Mixed Quasivariational-Like Inequalities , 2008 .

[30]  Dumitru Motreanu,et al.  Nonsmooth Variational Problems and Their Inequalities: Comparison Principles and Applications , 2010 .

[31]  Franco Giannessi,et al.  Regularization of non-coercive quasi variational inequalities , 2000 .

[32]  Fioravante Patrone,et al.  A characterization of tyhonov well-posedness for minimum problems, with applications to variational inequalities (∗) , 1981 .

[33]  Enrico Miglierina,et al.  Well-posedness and convexity in vector optimization , 2003, Math. Methods Oper. Res..

[34]  Yi-bin Xiao,et al.  Sub–super-solution method for a class of higher order evolution hemivariational inequalities ☆ , 2009 .

[35]  O. Chadli,et al.  Applications of Equilibrium Problems to a Class of Noncoercive Variational Inequalities , 2007 .

[36]  Ioan A. Rus,et al.  WELL-POSEDNESS IN THE GENERALIZED SENSE OF THE FIXED POINT PROBLEMS FOR MULTIVALUED OPERATORS , 2007 .

[37]  A. N. Tikhonov,et al.  On the stability of the functional optimization problem , 1966 .

[38]  Jen-Chih Yao,et al.  Regularized Equilibrium Problems with Application to Noncoercive Hemivariational Inequalities , 2004 .

[39]  B. Lemaire,et al.  Well-Posedness by Perturbations of Variational Problems , 2002 .

[40]  Nan-Jing Huang,et al.  Generalized quasi-variational-like hemivariational inequalities , 2008 .

[41]  Georges Zaccour,et al.  Decision and control in management science , 2002 .

[42]  P. D. Panagiotopoulos,et al.  Mathematical Theory of Hemivariational Inequalities and Applications , 1994 .

[43]  D. Goeleven,et al.  Well-posed hemivariational inequalities , 1995 .

[44]  F. Browder.  Nonlinear functional analysis and its applications , 1986 .

[45]  X. X. Huang,et al.  Extended and strongly extended well-posedness of set-valued optimization problems , 2001, Math. Methods Oper. Res..

[46]  Nan-Jing Huang,et al.  Metric characterizations of α-well-posedness for symmetric quasi-equilibrium problems , 2009, J. Glob. Optim..