Equilibrium Problems Nonsmooth Optimization and Variational Inequality Models [Paperback]

The aim of the book is to cover the three fundamental aspects of research in equilibrium problems: the statement problem and its formulation using mainly variational methods, its theoretical solution by means of classical and new variational tools, the calculus of solutions and applications in concrete cases. The book shows how many equilibrium problems follow a general law (the so-called user equilibrium condition). Such law allows us to express the problem in terms of variational inequalities. Variational inequalities provide a powerful methodology, by which existence and calculation of the solution can be obtained.

The aim of the book is to cover the three fundamental aspects of research in equilibrium problems: the statement problem and its formulation using mainly variational methods, its theoretical solution by means of classical and new variational tools, the calculus of solutions and applications in concrete cases. The book shows how many equilibrium problems follow a general law (the so-called user equilibrium condition). Such law allows us to express the problem in terms of variational inequalities. Variational inequalities provide a powerful methodology, by which existence and calculation of the solution can be obtained.

Preface.On the numerical solution of finite-dimensional variational inequalities by an interior point method; S. Bellavia, M.G. Gasparo.Fixed points in ordered Banach spaces and applications to elliptic boundary-value problems; G. Bonanno, S. Marano.A theorem of the alternative for linear control systems; P. Cubiotti.Variational inequalities for static equilibrium market. Lagrangean function and duality; P. Daniele.On dynamical equilibrium problems and variational inequalities; P. Daniele, A. Maugeri.Nonlinear programming methods for solving optimal control problems; C. Durazzi, E. Galligani.Optimal flow pattern in road networks; P. Ferrari.On the strong solvability of a unilateral boundary value problelÛ