Differential Vector Variational Inequalities in Finite-Dimensional Spaces

In this paper, a differential vector variational inequality is introduced and studied in finite-dimensional Euclidean spaces. The existence of a Carathéodory weak solution for the differential vector variational inequality is presented under some suitable conditions. Furthermore, the upper semicontinuity and the lower semicontinuity of the solution sets for the differential variational inequality are established when both the mapping and the constraint set are perturbed by two different parameters.

[1]  Jong-Shi Pang,et al.  A Time-Stepping Complementarity Approach for Frictionless Systems of Rigid Bodies , 2002, SIAM J. Optim..

[2]  Donal O'Regan,et al.  Differential mixed variational inequalities in finite dimensional spaces , 2010 .

[3]  Pierre E. Dupont,et al.  Analysis of Rigid-Body Dynamic Models for Simulation of Systems With Frictional Contacts , 2001 .

[4]  L. Q. Anh,et al.  Semicontinuity of the solution set of parametric multivalued vector quasiequilibrium problems , 2004 .

[5]  S. J. Li,et al.  Stability of weak vector variational inequality , 2009 .

[6]  J. Trinkle,et al.  Dynamic multi-rigid-body systems with concurrent distributed contacts , 2001, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[7]  B. Brogliato.  Nonsmooth Mechanics: Models, Dynamics and Control , 1999 .

[8]  Mihai Anitescu,et al.  A constraint‐stabilized time‐stepping approach for rigid multibody dynamics with joints, contact and friction , 2004 .

[9]  W. Heemels,et al.  Consistency of a time-stepping method for a class of piecewise-linear networks , 2002 .

[10]  A. Nagurney,et al.  Projected Dynamical Systems and Evolutionary Variational Inequalities via Hilbert Spaces with Applications1 , 2005 .

[11]  Jen-Chih Yao,et al.  Existence of Solutions for Generalized Vector Variational-like Inequalities , 2008 .

[12]  Jong-Shi Pang,et al.  Non-Zenoness of a class of differential quasi-variational inequalities , 2010, Math. Program..

[13]  Nan-Jing Huang,et al.  On Vector Variational Inequalities in Reflexive Banach Spaces , 2005, J. Glob. Optim..

[14]  S. J. Li,et al.  On the solution semicontinuity to a parametric generalized vector quasivariational inequality , 2010, Comput. Math. Appl..

[15]  Jen-Chih Yao,et al.  Semicontinuity of Solution Mappings of Parametric Generalized Vector Equilibrium Problems , 2008 .

[16]  Lorenz T. Biegler,et al.  Parameter estimation in metabolic flux balance models for batch fermentation—Formulation & Solution using Differential Variational Inequalities (DVIs) , 2006, Ann. Oper. Res..

[17]  K. Fan.  A generalization of Tychonoff's fixed point theorem , 1961 .

[18]  David E. Stewart,et al.  Uniqueness for index-one differential variational inequalities , 2008 .

[19]  Jong-Shi Pang,et al.  A semi‐implicit time‐stepping model for frictional compliant contact problems , 2004 .

[20]  D. Stewart.  Convergence of a Time‐Stepping Scheme for Rigid‐Body Dynamics and Resolution of Painlevé's Problem , 1998 .

[21]  D. Stewart,et al.  Time-stepping for three-dimensional rigid body dynamics , 1999 .

[22]  Kenji Kimura,et al.  Semicontinuity of solution mappings of parametric generalized strong vector equilibrium problems , 2008 .

[23]  Jiang-hua Fan,et al.  Stability analysis for variational inequality in reflexive Banach spaces , 2008 .

[24]  Y. H. Cheng,et al.  Global Stability Results for the Weak Vector Variational Inequality , 2005, J. Glob. Optim..

[25]  Phan Quoc Khanh,et al.  Upper Semicontinuity of the Solution set to Parametric Vector Quasivariational Inequalities , 2005, J. Glob. Optim..

[26]  M. Kanat Camlibel,et al.  On Linear Passive Complementarity Systems , 2002, Eur. J. Control.

[27]  Xiaoqi Yang,et al.  Vector Optimization: Set-Valued and Variational Analysis , 2005 .

[28]  F. Giannessi.  Vector Variational Inequalities and Vector Equilibria: Mathematical Theories , 2011 .

[29]  W. P. M. H. Heemels,et al.  Linear Complementarity Systems , 2000, SIAM J. Appl. Math..

[30]  Kok Lay Teo,et al.  On the Stability of Generalized Vector Quasivariational Inequality Problems , 2002 .

[31]  Jong-Shi Pang,et al.  Differential variational inequalities , 2008, Math. Program..

[32]  Xiaoqi Yang,et al.  Gap Functions and Existence of Solutions to Set-Valued Vector Variational Inequalities , 2002 .

[33]  W. Rudin.  Real and complex analysis , 1968 .

[34]  Jong-Shi Pang,et al.  Strongly Regular Differential Variational Systems , 2007, IEEE Transactions on Automatic Control.

[35]  W. P. M. H. Heemels,et al.  Projected dynamical systems in a complementarity formalism , 1999, Oper. Res. Lett..

[36]  Y. Chiang,et al.  Semicontinuous Mappings into T.V.S. with Applications to Mixed Vector Variational-Like Inequalities , 2005, J. Glob. Optim..

[37]  S. J. Li,et al.  Existence of solutions for a generalized vector quasivariational inequality , 1996 .