This book discusses a new discipline, variational analysis, which contains the calculus of variations, differential calculus, optimization, and variational inequalities. To such classic branches of mathematics, variational analysis provides a uniform theoretical base that represents a powerful tool for the applications. The contributors are among the best experts in the field.

A thorough treatment of the latest developments in the field of variational analysis

1.- The Work of G. Stampacchia in Variational Inequalities.- In Memory of Guido Stampacchia.- The Collaboration between Guido Stampacchia and Jacques-Louis Lions on Variational Inequalities.- In Memory of Guido Stampacchia.- Guido Stampacchia.- Memories of Guido Stampacchia.- In Memory of Guido Stampacchia.- Guido Stampacchia, My Father.- 2.- Convergence and Stability of a Regularization Method for Maximal Monotone Inclusions and Its Applications to Convex Optimization.- Partitionable Mixed Variational Inequalities.- Irreducibility of the Transition Semigroup Associated with the Two Phase Stefan Problem.- On Some Boundary Value Problems for Flows with Shear Dependent Viscosity.- Homogenization of Systems of Partial Differential Equations.- About the Duality Gap in Vector Optimization.- Separation of Convex Cones and Extremal Problems.- Infinitely Many Solutions for the Dirichlet Problem Via a Variational Principle of Ricceri.- A Density Result on the Space VMO ?.- Linear Complementarity Since 1978.- Variational Inequalities in Vector Optimization.- Variational Inequalities for General Evolutionary Financial Equilibrium.- Variational Control Problems with Constraints Via Exact Penalization.- Continuous Sets and Non-Attaining Fuctionals in Reflexive Banach Spaces.- Existence and Multiplicity Results for a Non Linear Hammerstein Integral Equation.- Differentiability of Weak Solutions of Nonlinear Second Order Parabolic Systems with Quadratic Growth and Non Linearity q ? 2.- An Optimization Problem with an Equilibrium Constraint in Urban Transport.- Sharp Estimates for Green's Functions: Singular Cases.- First-Order Conditions for C 0,1 Constrained Vector Optimization.- Global Regularity for Solutions to Dirichlet Problem for Elliptic Systems with Nonlinearity q ? 2and with Natural Growth.- Optimality Conditions for Generalized Complementarity Problems.- Variational Inequalities for Time Dependent Financial Equilibrium with Price Constraints.- Remarks About Diffusion Mediated Transport: Thinking About Motion in Small Systems.- Augmented Lagrangian and Nonlinear Semidefinite Programs.- Optimality Alternative: a Non-Variational Approach to Necessary Conditions.- A Variational Inequality Scheme for Determining an Economic Equilibrium of Classical or Extended Type.- On Time Dependent Vector Equilibrium Problems.- On Some Nonstandard Dynamic Programming Problems of Control Theory.- Properties of Gap Function for Vector Variational Inequality.- Zero Gravity Capillary Surfaces and Integral Estimates.- Asymptotically Critical Points and Multiple Solutions in the Elastic Bounce Problem.- A Branch-and-Cut to the Point-to-Point Connection Problem on Multicast Networks.- Variational Inequality and Evolutionary Market Disequilibria: The Case of Quantity Formulation.- Numerical Approximation of Free Boundary Problem by Variational Inequalities. Application to Semiconductor Devices.- Sensitivity Analysis for Variational Systems.- Stable Critical Points for the Ginzburg Landau Functional on Some Plane Domains.- The Distance Function to the Boundary and Singular Set of Viscosity Solutions of Hamilton-Jacobi Equation.- L P-Regularity for Poincaré Problem and Applications.- Minimal Fractions of Compact Convex Sets.- On Generalized Variational Inequalities.- Bounded (Hausdorff) Convergence: Basic Facts and Applications.- Control Processes with Distributed Parameters in Unbounded Sets. Approximate Controllability with Variable Initial Locus.- Well Posedness and Optimization Problems.- Semismooth Newton Methods for Shape-Preserving Interpolation,Option Price and Semi-Infinite Programs.- Hölder Regularity Results for Solutions of Parabolic Equations.- Survey on the Fenchel Problem of Level Sets.- Integral Functionals on Sobolev Spaces Having Multiple Local Minima.- Aspects of the Projector on Prox-Regular Sets.- Application of Optimal Control Theory to Dynamic Soaring of Seabirds.- On the Convergence of the Matrices Associated to the Adjugate Jacobians.- Quasi-Variatonal Inequalities Applied to Retarded Equilibria in Time-Dependent Traffic Problems.- Higher Order Approximation Equations for the Primitive Equations of the Ocean.- Hahn-Banach Theorems and Maximal Monotonicity.- Concrete Problems and the General Theory of Extremum.- Numerical Solution for Pseudomonotone Variational Inequality Problems by Extragradient Methods.- Regularity and Existence Results for Degenerate Elliptic Operators.- Vector Variational Inequalities and Dynamic Traffic Equilibria.- A New Proof of the Maximal Monotonicity of the Sum Using the Fitzpatrick Function.