The volume, devoted to variational analysis and its applications, collects selected and refereed contributions, which provide an outline of the field.
The meeting of the title “Equilibrium Problems and Variational Models”, which was held in Erice (Sicily) in the period June 23 – July 2 2000, was the occasion of the presentation of some of these papers; other results are a consequence of a fruitful and constructive atmosphere created during the meeting.
New results, which enlarge the field of application of variational analysis, are presented in the book; they deal with the vectorial analysis, time dependent variational analysis, exact penalization, high order derivatives, geometrie aspects, distance functions and log-quadratic proximal methodology.
The new theoretical results allow one to improve in a remarkable way the study of signifìcant problems arising from the applied sciences, as continuum model of transportation, unilateral problems, multicriteria spatial price models, network equilibrium problems and many others.
As noted in the previous book “Equilibrium Problems: Nonsmooth Optimiza.tion and Va.riational lnequality Models” , edited by F. Giannessi, A. Maugeri and P.M. Pardalos, Kluwer Academic Publishers, Vol. 58 (2001), the progress obtained by variational analysis has permitted to handle problems whose equilibrium conditions are not obtained by the minimization of a functional. These problems obey a more realistic equilibrium condition expressed by a generalized orthogonality (complementarity) condition, which enriches our knowledge of the equilibrium behaviour. Also this volume presents important examples of this formulation.
Finally, recent numerical methods complete this volume that, like the previous one, aims to treat problems from their statement up to the computation of their solutions.
Patrizia Daniele, University of Catania
Franco Giannessi, University of Pisa
Antonino Maugeri, University of Catania