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| Author | : Donald R. Smith |
| Publisher | : Courier Corporation |
| Total Pages | : 406 |
| Release | : 1998-01-01 |
| Genre | : Mathematics |
| ISBN | : 9780486404554 |
Highly readable text elucidates applications of the chain rule of differentiation, integration by parts, parametric curves, line integrals, double integrals, and elementary differential equations. 1974 edition.
| Author | : Andrej Cherkaev |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 561 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 1461211883 |
This book bridges a gap between a rigorous mathematical approach to variational problems and the practical use of algorithms of structural optimization in engineering applications. The foundations of structural optimization are presented in sufficiently simple form as to make them available for practical use.
| Author | : Dorin Bucur |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 218 |
| Release | : 2006-09-13 |
| Genre | : Mathematics |
| ISBN | : 0817644032 |
Shape optimization problems are treated from the classical and modern perspectives Targets a broad audience of graduate students in pure and applied mathematics, as well as engineers requiring a solid mathematical basis for the solution of practical problems Requires only a standard knowledge in the calculus of variations, differential equations, and functional analysis Driven by several good examples and illustrations Poses some open questions.
| Author | : Alexey F. Izmailov |
| Publisher | : Springer |
| Total Pages | : 587 |
| Release | : 2014-07-08 |
| Genre | : Business & Economics |
| ISBN | : 3319042475 |
This book presents comprehensive state-of-the-art theoretical analysis of the fundamental Newtonian and Newtonian-related approaches to solving optimization and variational problems. A central focus is the relationship between the basic Newton scheme for a given problem and algorithms that also enjoy fast local convergence. The authors develop general perturbed Newtonian frameworks that preserve fast convergence and consider specific algorithms as particular cases within those frameworks, i.e., as perturbations of the associated basic Newton iterations. This approach yields a set of tools for the unified treatment of various algorithms, including some not of the Newton type per se. Among the new subjects addressed is the class of degenerate problems. In particular, the phenomenon of attraction of Newton iterates to critical Lagrange multipliers and its consequences as well as stabilized Newton methods for variational problems and stabilized sequential quadratic programming for optimization. This volume will be useful to researchers and graduate students in the fields of optimization and variational analysis.
| Author | : Dimitrios C. Kravvaritis |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 384 |
| Release | : 2020-04-06 |
| Genre | : Mathematics |
| ISBN | : 3110647451 |
This well-thought-out book covers the fundamentals of nonlinear analysis, with a particular focus on variational methods and their applications. Starting from preliminaries in functional analysis, it expands in several directions such as Banach spaces, fixed point theory, nonsmooth analysis, minimax theory, variational calculus and inequalities, critical point theory, monotone, maximal monotone and pseudomonotone operators, and evolution problems.
| Author | : Jonathan Borwein |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 368 |
| Release | : 2006-06-18 |
| Genre | : Mathematics |
| ISBN | : 0387282718 |
Borwein is an authority in the area of mathematical optimization, and his book makes an important contribution to variational analysis Provides a good introduction to the topic
| Author | : Kevin W. Cassel |
| Publisher | : Cambridge University Press |
| Total Pages | : 433 |
| Release | : 2013-07-22 |
| Genre | : Mathematics |
| ISBN | : 1107022584 |
This book reflects the strong connection between calculus of variations and the applications for which variational methods form the foundation.
| Author | : J.L. Troutman |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 373 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1468401580 |
The calculus of variations, whose origins can be traced to the works of Aristotle and Zenodoros, is now Ii vast repository supplying fundamental tools of exploration not only to the mathematician, but-as evidenced by current literature-also to those in most branches of science in which mathematics is applied. (Indeed, the macroscopic statements afforded by variational principles may provide the only valid mathematical formulation of many physical laws. ) As such, it retains the spirit of natural philosophy common to most mathematical investigations prior to this century. How ever, it is a discipline in which a single symbol (b) has at times been assigned almost mystical powers of operation and discernment, not readily subsumed into the formal structures of modern mathematics. And it is a field for which it is generally supposed that most questions motivating interest in the subject will probably not be answerable at the introductory level of their formulation. In earlier articles,1,2 it was shown through several examples that a complete characterization of the solution of optimization problems may be available by elementary methods, and it is the purpose of this work to explore further the convexity which underlay these individual successes in the context of a full introductory treatment of the theory of the variational calculus. The required convexity is that determined through Gateaux variations, which can be defined in any real linear space and which provide an unambiguous foundation for the theory.
| Author | : Dumitru Motreanu |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 400 |
| Release | : 2003-05-31 |
| Genre | : Mathematics |
| ISBN | : 9781402013850 |
This book reflects a significant part of authors' research activity dur ing the last ten years. The present monograph is constructed on the results obtained by the authors through their direct cooperation or due to the authors separately or in cooperation with other mathematicians. All these results fit in a unitary scheme giving the structure of this work. The book is mainly addressed to researchers and scholars in Pure and Applied Mathematics, Mechanics, Physics and Engineering. We are greatly indebted to Viorica Venera Motreanu for the careful reading of the manuscript and helpful comments on important issues. We are also grateful to our Editors of Kluwer Academic Publishers for their professional assistance. Our deepest thanks go to our numerous scientific collaborators and friends, whose work was so important for us. D. Motreanu and V. Radulescu IX Introduction The present monograph is based on original results obtained by the authors in the last decade. This book provides a comprehensive expo sition of some modern topics in nonlinear analysis with applications to the study of several classes of boundary value problems. Our framework includes multivalued elliptic problems with discontinuities, variational inequalities, hemivariational inequalities and evolution problems. The treatment relies on variational methods, monotonicity principles, topo logical arguments and optimization techniques. Excepting Sections 1 and 3 in Chapter 1 and Sections 1 and 3 in Chapter 2, the material is new in comparison with any other book, representing research topics where the authors contributed. The outline of our work is the following.
| Author | : Michael Ulbrich |
| Publisher | : SIAM |
| Total Pages | : 315 |
| Release | : 2011-07-28 |
| Genre | : Mathematics |
| ISBN | : 1611970687 |
A comprehensive treatment of semismooth Newton methods in function spaces: from their foundations to recent progress in the field. This book is appropriate for researchers and practitioners in PDE-constrained optimization, nonlinear optimization and numerical analysis, as well as engineers interested in the current theory and methods for solving variational inequalities.
