Foundations of Optimization - Couverture souple

Güler, Osman

Couverture souple

ISBN 10 : 1461426472 ISBN 13 : 9781461426479

Editeur : Springer, 2012

Synopsis

Optimization is everywhere. It is human nature to seek the best option among all that are available. Nature, too, seems to be guided by optimization|many laws of nature have a variational character. Among geometric gures in the plane with a xed perimeter, the circle has the greatest area. Such isoperim- ric problems involving geometric gures date back to ancient Greece. Fermat s principle, discovered in 1629, stating that the tangent line is horizontal at a minimum point, seems to have in uenced the development of calculus. The proofs of Rolle s theorem and the mean value theorem in calculus use the Weierstrass theorem on the existence of maximizers and minimizers. The - troduction of the brachistochrone problem in 1696 by Johann Bernoulli had a tremendous impact on the development of the calculus of variations and in uenced the development of functional analysis. The variational character of laws of mechanics and optics were discovered in the seventeenth and ei- teenth centuries. Euler and Lagrange forged the foundations of the calculus of variations in the eighteenth century. In the nineteenth century, Riemann used Dirichlet s principle, which has a variational character, in his investigations in complex analysis. The simplex method for linear programming was disc- ered shortly after the advent of computers in the 1940s, and in uenced the subsequent development of mathematical programming. The emergence of the theory of optimal control in the 1950s was in response to the need for contr- ling space vehicles and various industrial processes.

A propos du livre

À propos de la quatrième de couverture

The book gives a detailed and rigorous treatment of the theory of optimization (unconstrained optimization, nonlinear programming, semi-infinite programming, etc.) in finite-dimensional spaces. The fundamental results of convexity theory and the theory of duality in nonlinear programming and the theories of linear inequalities, convex polyhedra, and linear programming are covered in detail. Over two hundred, carefully selected exercises should help the students master the material of the book and give further insight. Some of the most basic results are proved in several independent ways in order to give flexibility to the instructor. A separate chapter gives extensive treatments of three of the most basic optimization algorithms (the steepest-descent method, Newton s method, the conjugate-gradient method). The first chapter of the book introduces the necessary differential calculus tools used in the book. Several chapters contain more advanced topics in optimization such as Ekeland s epsilon-variational principle, a deep and detailed study of separation properties of two or more convex sets in general vector spaces, Helly s theorem and its applications to optimization, etc. The book is suitable as a textbook for a first or second course in optimization at the graduate level. It is also suitable for self-study or as a reference book for advanced readers. The book grew out of author s experience in teaching a graduate level one-semester course a dozen times since 1993.Osman Guler is a Professor in the Department of Mathematics and Statistics at University of Maryland, Baltimore County. His research interests include mathematical programming, convex analysis, complexity of optimization problems, and operations research.

Détails de l'édition

• Éditeur: Springer
• Date d'édition: 2012
• Langue: anglais
• ISBN 10: 1461426472
• ISBN 13: 9781461426479
• Reliure: Broché
• Nombre de pages: 460
• Coordonnées du fabricant: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3; Heidelberg; 69115; Allemagne