Vector Variational Inequalities and Vector Equilibria: Mathematical Theories: 38 (Nonconvex Optimization and Its Applications, 38) - Hardcover

Hardcover

ISBN 10: 0792360265 ISBN 13: 9780792360261

Publisher: Kluwer Academic Publishers, 1999

Synopsis

In the fifties and sixties, several real problems, old and new, especially in Physics, Mechanics, Fluidodynamics, Structural Engi­ neering, have shown the need of new mathematical models for study­ ing the equilibrium of a system. This has led to the formulation of Variational Inequalities (by G. Stampacchia), and to the develop­ ment of Complementarity Systems (by W.S. Dorn, G.B. Dantzig, R.W. Cottle, O.L. Mangasarian et al.) with important applications in the elasto-plastic field (initiated by G. Maier). The great advan­ tage of these models is that the equilibrium is not necessarily the extremum of functional, like energy, so that no such functional must be supposed to exist. In the same decades, in some fields like Control Theory, Net­ works, Industrial Systems, Logistics, Management Science, there has been a strong request of mathmatical models for optimizing situa­ tions where there are concurrent objectives, so that Vector Optimiza­ tion (initiated by W. Pareto) has received new impetus. With regard to equilibrium problems, Vector Optimization has the above - mentioned drawback of being obliged to assume the exis­ tence of a (vector) functional. Therefore, at the end of the seventies the study of Vector Variational Inequalities began with the scope of exploiting the advantages of both variational and vector models. This volume puts together most of the recent mathematical results in Vector Variational Inequalities with the purpose of contributing to further research.

About this title

Synopsis

This book deals with the mathematical theory of vector variational inequalities with special reference to equilibrium problems. Such models have been introduced recently to study new problems from mechanics, structural engineering, networks, and industrial management, and to revisit old ones. The common feature of these problems is that given by the presence of concurrent objectives and by the difficulty of identifying a global functional (like energy) to be extremized. The vector variational inequalities have the advantage of both the variational ones and vector optimization which are found as special cases. Among several applications, the equilibrium flows on a network receive special attention. The book is addressed to academic researchers as well as industrial ones, in the fields of mathematics, engineering, mathematical programming, control theory, operations research, computer science, and economics.

Edition details

• Publisher: Kluwer Academic Publishers
• Publication date: 1999
• Language: English
• ISBN 10: 0792360265
• ISBN 13: 9780792360261
• Binding: Hardcover
• Number of pages: 540
• Editor: Giannessi F.