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Variational Inequalities (variational + inequality)
Selected Abstractshp -Adaptive Finite Element Methods for Variational InequalitiesPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2008Andreas SchröderArticle first published online: 25 FEB 200 In this work, we combine an hp,adaptive strategy with a posteriori error estimates for variational inequalities, which are given by contact problems. The a posteriori error estimates are obtained using a general approach based on the saddle point formulation of contact problems and making use of a yposteriori error estimates for variational equations. Error estimates are presented for obstacle problems and Signorini problems with friction. Numerical experiments confirm the reliability of the error estimates for finite elements of higher order. The use of the hp,adaptive strategy leads to meshes with the same characteristics as geometric meshes and to exponential convergence. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Adaptive computational methods for variational inequalities based on mixed formulationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2006F. T. SuttmeierArticle first published online: 27 APR 200 Abstract This work describes concepts for a posteriori error estimation and adaptive mesh design for finite element models where the solution is subjected to inequality constraints. These methods are developed here for several model problems. Based on these examples, unified frameworks are proposed, which provide a systematic way of adaptive error control for problems stated in form of variational inequalities. Copyright © 2006 John Wiley & Sons, Ltd. [source] Numerical inclusion methods of solutions for variational inequalitiesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2002C. S. Ryoo Abstract We consider a numerical method that enables us to verify the existence of solutions for variational inequalities. This method is based on the infinite dimensional fixed point theorems and explicit error estimates for finite element approximations. Using the finite element approximations and explicit a priori error estimates, we present an effective verification procedure that through numerical computation generates a set which includes the exact solution. Copyright © 2002 John Wiley & Sons, Ltd. [source] Private road competition and equilibrium with traffic equilibrium constraintsJOURNAL OF ADVANCED TRANSPORTATION, Issue 1 2009Hai Yang Abstract Toll road competition is one of the important issues under a build-operate-transfer (BOT) scheme, which is being encountered nowadays in many cities. When there are two or more competing firms and each firm operates a competitive toll road, their profits are interrelated due to the competitors' choices and demand inter-dependence in the network. In this paper we develop game-theoretic approaches to the study of the road network, on which multiple toll roads are operated by competitive private firms. The strategic interactions and market equilibria among the private firms are analyzed both in determining their supply (road capacity) and price (toll level) over the network. The toll road competition problems in general traffic equilibrium networks are formulated as an equilibrium program with equilibrium constraints or bi-level variational inequalities. Heuristic solution methods are proposed and their convergences are demonstrated with simple network examples. It is shown that private pricing and competition can be both profitable and welfare-improving. [source] A class of implicit variational inequalities and applications to frictional contactMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 14 2009Anca Capatina Abstract This paper deals with the mathematical and numerical analysis of a class of abstract implicit evolution variational inequalities. The results obtained here can be applied to a large variety of quasistatic contact problems in linear elasticity, including unilateral contact or normal compliance conditions with friction. In particular, a quasistatic unilateral contact problem with nonlocal friction is considered. An algorithm is derived and some numerical examples are presented. Copyright © 2009 John Wiley & Sons, Ltd. [source] A system of variational inequalities arising from finite expiry Russian option with two regimesMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 13 2009Zhou Yang Abstract In this paper we consider a system of variational inequalities arising from the value of finite expiry Russian option with two regimes. We achieve the existence and uniqueness of the solution to the problem. Moreover, we show that the free boundaries are infinitely differentiable and monotonic with respect to time and some parameters in this system, as well as the mutual relationship between the solutions in two regimes. Moreover, we establish the bound of the free boundaries and analyze their property as time converges to infinite. Copyright © 2009 John Wiley & Sons, Ltd. [source] The play operator on the rectifiable curves in a Hilbert spaceMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 11 2008Vincenzo Recupero Abstract The vector play operator is the solution operator of a class of evolution variational inequalities arising in continuum mechanics. For regular data, the existence of solutions is easily obtained from general results on maximal monotone operators. If the datum is a continuous function of bounded variation, then the existence of a weak solution is usually proved by means of a time discretization procedure. In this paper we give a short proof of the existence of the play operator on rectifiable curves making use of basic facts of measure theory. We also drop the separability assumptions usually made by other authors. Copyright © 2007 John Wiley & Sons, Ltd. [source] Mathematical analysis of some new Reynolds-rod elastohydrodynamic modelsMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 15 2001G. Bayada In this paper, some new elastohydrodynamic Reynolds-rod models are posed to obtain the existence of solution (the lubricant pressure and the elastic rod displacement). More precisely, a sign restriction on fluid pressure for cavitation modelling and different unilateral conditions on the rod displacement associated with a rigid structure coating are formulated in terms of coupled variational inequalities. The particular hinged or clamped boundary conditions on the rod displacement require different techniques to prove the existence of solution. Besides nearly linear coupled problems, two non-linear rod problems including curvature effects are analysed. Mainly, regularity results and L, estimates for the solution of variational inequalities and fixed-point theorems lead to the existence results for the various coupled models. Copyright © 2001 John Wiley & Sons, Ltd. [source] Generalized multivalued nonlinear quasivariational inclusionsMATHEMATISCHE NACHRICHTEN, Issue 1 2003Zeqing Liu Abstract In this paper, we introduce and study a few classes of generalized multivalued nonlinear quasivariational inclusions and generalized nonlinear quasivariational inequalities, which include many classes of variational inequalities, quasivariational inequalities and variational inclusions as special cases. Using the resolvent operator technique for maximal monotone mapping, we construct some new iterative algorithms for finding the approximate solutions of these classes of quasivariational inclusions and quasivariational inequalities. We establish the existence of solutions for this generalized nonlinear quasivariational inclusions involving both relaxed Lipschitz and strongly monotone and generalized pseudocontractive mappings and obtain the convergence of iterative sequences generated by the algorithms. Under certain conditions, we derive the existence of a unique solution for the generalized nonlinear quasivariational inequalities and obtain the convergence and stability results of the Noor type perturbed iterative algorithm. The results proved in this paper represent significant refinements and improvements of the previously known results in this area. [source] Projector preconditioning for partially bound-constrained quadratic optimizationNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 10 2007Marta Domorádová Abstract Preconditioning by a conjugate projector is combined with the recently proposed modified proportioning with reduced gradient projection (MPRGP) algorithm for the solution of bound-constrained quadratic programming problems. If applied to the partially bound-constrained problems, such as those arising from the application of FETI-based domain decomposition methods to the discretized elliptic boundary variational inequalities, the resulting algorithm is shown to have better bound on the rate of convergence than the original MPRGP algorithm. The performance of the algorithm is illustrated on the solution of a model boundary variational inequality. Copyright © 2007 John Wiley & Sons, Ltd. [source] Bi-criteria optimal control of redundant robot manipulators using LVI-based primal-dual neural networkOPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 3 2010Binghuang Cai Abstract In this paper, a bi-criteria weighting scheme is proposed for the optimal motion control of redundant robot manipulators. To diminish the discontinuity phenomenon of pure infinity-norm velocity minimization (INVM) scheme, the proposed bi-criteria redundancy-resolution scheme combines the minimum kinetic energy scheme and the INVM scheme via a weighting factor. Joint physical limits such as joint limits and joint-velocity limits could also be incorporated simultaneously into the scheme formulation. The optimal kinematic control scheme can be reformulated finally as a quadratic programming (QP) problem. As the real-time QP solver, a primal-dual neural network (PDNN) based on linear variational inequalities (LVI) is developed as well with a simple piecewise-linear structure and global exponential convergence to optimal solutions. Since the LVI-based PDNN is matrix-inversion free, it has higher computational efficiency in comparison with dual neural networks. Computer simulations performed based on the PUMA560 manipulator illustrate the validity and advantages of such a bi-criteria neural optimal motion-control scheme for redundant robots. Copyright © 2009 John Wiley & Sons, Ltd. [source] A space-time network for telecommuting versus commuting decision-making,PAPERS IN REGIONAL SCIENCE, Issue 4 2003Anna Nagurney Transportation and telecommunication networks; telecommuting and commuting; space-time networks; variational inequalities Abstract. In this article, we develop a theoretical framework for the study of telecommuting versus commuting decision-making over a fixed time horizon, such as a work week through the use of a space-time network to conceptualize the decision-makers' choices over space and time. The decision-makers are multiclass and multicriteria ones and perceive the criteria of travel cost, travel time, and opportunity cost in an individual fashion. The model is a network equilibrium type and allows for the prediction of the equilibrium flows and, hence, the number of periods that members of each class of decision-makers will telecommute or commute. Qualitative properties of the equilibrium are obtained and an algorithm is given, along with convergence results, and applied to numerical examples. [source] hp -Adaptive Finite Element Methods for Variational InequalitiesPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2008Andreas SchröderArticle first published online: 25 FEB 200 In this work, we combine an hp,adaptive strategy with a posteriori error estimates for variational inequalities, which are given by contact problems. The a posteriori error estimates are obtained using a general approach based on the saddle point formulation of contact problems and making use of a yposteriori error estimates for variational equations. Error estimates are presented for obstacle problems and Signorini problems with friction. Numerical experiments confirm the reliability of the error estimates for finite elements of higher order. The use of the hp,adaptive strategy leads to meshes with the same characteristics as geometric meshes and to exponential convergence. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] hp -Mortar boundary element method for two-body contact problems with frictionMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 17 2008Alexey Chernov Abstract We construct a novel hp -mortar boundary element method for two-body frictional contact problems for nonmatched discretizations. The contact constraints are imposed in the weak sense on the discrete set of Gauss,Lobatto points using the hp -mortar projection operator. The problem is reformulated as a variational inequality with the Steklov,Poincaré operator over a convex cone of admissible solutions. We prove an a priori error estimate for the corresponding Galerkin solution in the energy norm. Due to the nonconformity of our approach, the Galerkin error is decomposed into the approximation error and the consistency error. Finally, we show that the Galerkin solution converges to the exact solution as ,,((h/p)1/4) in the energy norm for quasiuniform discretizations under mild regularity assumptions. We solve the Galerkin problem with a Dirichlet-to-Neumann algorithm. The original two-body formulation is rewritten as a one-body contact subproblem with friction and a one-body Neumann subproblem. Then the original two-body frictional contact problem is solved with a fixed point iteration. Copyright © 2008 John Wiley & Sons, Ltd. [source] Numerical simulation of the non-linear crack problem with non-penetrationMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 2 2004Victor A. Kovtunenko Abstract Here the numerical simulation of some plane Lamé problem with a rectilinear crack under non-penetration condition is presented. The corresponding solids are assumed to be isotropic and homogeneous as well as bonded. The non-linear crack problem is formulated as a variational inequality. We use penalty iteration and the finite-element method to calculate numerically its approximate solution. Applying analytic formulas obtained from shape sensitivity analysis, we calculate then energetic and stress characteristics of the solution, and describe the quasistatic propagation of the crack under linear loading. The results are presented in comparison with the classical, linear crack problem, when interpenetration between the crack faces may occur. Copyright © 2004 John Wiley & Sons, Ltd. [source] Analysis of a time discretization for an implicit variational inequality modelling dynamic contact problems with frictionMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 7 2001Jean-Marc Ricaud Abstract Some dynamic contact problems with friction can be formulated as an implicit variational inequality. A time discretization of such an inequality is given here, thus giving rise to a so-called incremental solution. The convergence of the incremental solution is established, and then the limit is shown to be the unique solution of the variational inequality. This paper contains therefore not only some new results concerning the numerical aspect of some models of contact and friction but also a constructive existence result. Copyright © 2001 John Wiley & Sons, Ltd. [source] OPTIMAL HARVESTING OF A SPATIALLY EXPLICIT FISHERY MODELNATURAL RESOURCE MODELING, Issue 2 2009WANDI DING Abstract We consider an optimal fishery harvesting problem using a spatially explicit model with a semilinear elliptic PDE, Dirichlet boundary conditions, and logistic population growth. We consider two objective functionals: maximizing the yield and minimizing the cost or the variation in the fishing effort (control). Existence, necessary conditions, and uniqueness for the optimal harvesting control for both cases are established. Results for maximizing the yield with Neumann (no-flux) boundary conditions are also given. The optimal control when minimizing the variation is characterized by a variational inequality instead of the usual algebraic characterization, which involves the solutions of an optimality system of nonlinear elliptic partial differential equations. Numerical examples are given to illustrate the results. [source] Projector preconditioning for partially bound-constrained quadratic optimizationNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 10 2007Marta Domorádová Abstract Preconditioning by a conjugate projector is combined with the recently proposed modified proportioning with reduced gradient projection (MPRGP) algorithm for the solution of bound-constrained quadratic programming problems. If applied to the partially bound-constrained problems, such as those arising from the application of FETI-based domain decomposition methods to the discretized elliptic boundary variational inequalities, the resulting algorithm is shown to have better bound on the rate of convergence than the original MPRGP algorithm. The performance of the algorithm is illustrated on the solution of a model boundary variational inequality. Copyright © 2007 John Wiley & Sons, Ltd. [source] Minimising the variance under convex constraintsPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2003Ulrich Hirth Dr. rer. nat. I treat the problem of minimising the variance functional on a certain closed convex subset of L2(P) by means of the variational inequality, obtaining an explicit formula for the solution and analysing the dependence of the solution on the initial data. [source] | ||||||||||||||||