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Author | : Hubertus Th. Jongen |
Publisher | : Springer Science & Business Media |
Total Pages | : 516 |
Release | : 2013-12-11 |
Genre | : Mathematics |
ISBN | : 1461500176 |
Download Nonlinear Optimization in Finite Dimensions Book in PDF, ePub and Kindle
At the heart of the topology of global optimization lies Morse Theory: The study of the behaviour of lower level sets of functions as the level varies. Roughly speaking, the topology of lower level sets only may change when passing a level which corresponds to a stationary point (or Karush-Kuhn Tucker point). We study elements of Morse Theory, both in the unconstrained and constrained case. Special attention is paid to the degree of differentiabil ity of the functions under consideration. The reader will become motivated to discuss the possible shapes and forms of functions that may possibly arise within a given problem framework. In a separate chapter we show how certain ideas may be carried over to nonsmooth items, such as problems of Chebyshev approximation type. We made this choice in order to show that a good under standing of regular smooth problems may lead to a straightforward treatment of "just" continuous problems by means of suitable perturbation techniques, taking a priori nonsmoothness into account. Moreover, we make a focal point analysis in order to emphasize the difference between inner product norms and, for example, the maximum norm. Then, specific tools from algebraic topol ogy, in particular homology theory, are treated in some detail. However, this development is carried out only as far as it is needed to understand the relation between critical points of a function on a manifold with structured boundary. Then, we pay attention to three important subjects in nonlinear optimization.
Author | : Josef Stoer |
Publisher | : Springer Science & Business Media |
Total Pages | : 306 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3642462162 |
Download Convexity and Optimization in Finite Dimensions I Book in PDF, ePub and Kindle
Dantzig's development of linear programming into one of the most applicable optimization techniques has spread interest in the algebra of linear inequalities, the geometry of polyhedra, the topology of convex sets, and the analysis of convex functions. It is the goal of this volume to provide a synopsis of these topics, and thereby the theoretical back ground for the arithmetic of convex optimization to be treated in a sub sequent volume. The exposition of each chapter is essentially independent, and attempts to reflect a specific style of mathematical reasoning. The emphasis lies on linear and convex duality theory, as initiated by Gale, Kuhn and Tucker, Fenchel, and v. Neumann, because it represents the theoretical development whose impact on modern optimi zation techniques has been the most pronounced. Chapters 5 and 6 are devoted to two characteristic aspects of duality theory: conjugate functions or polarity on the one hand, and saddle points on the other. The Farkas lemma on linear inequalities and its generalizations, Motzkin's description of polyhedra, Minkowski's supporting plane theorem are indispensable elementary tools which are contained in chapters 1, 2 and 3, respectively. The treatment of extremal properties of polyhedra as well as of general convex sets is based on the far reaching work of Klee. Chapter 2 terminates with a description of Gale diagrams, a recently developed successful technique for exploring polyhedral structures.
Author | : Osman Güler |
Publisher | : Springer Science & Business Media |
Total Pages | : 445 |
Release | : 2010-08-03 |
Genre | : Business & Economics |
ISBN | : 0387684077 |
Download Foundations of Optimization Book in PDF, ePub and Kindle
This book covers the fundamental principles of optimization in finite dimensions. It develops the necessary material in multivariable calculus both with coordinates and coordinate-free, so recent developments such as semidefinite programming can be dealt with.
Author | : Jonathan Borwein |
Publisher | : Springer Science & Business Media |
Total Pages | : 316 |
Release | : 2010-05-05 |
Genre | : Mathematics |
ISBN | : 0387312560 |
Download Convex Analysis and Nonlinear Optimization Book in PDF, ePub and Kindle
Optimization is a rich and thriving mathematical discipline, and the underlying theory of current computational optimization techniques grows ever more sophisticated. This book aims to provide a concise, accessible account of convex analysis and its applications and extensions, for a broad audience. Each section concludes with an often extensive set of optional exercises. This new edition adds material on semismooth optimization, as well as several new proofs.
Author | : Johannes Jahn |
Publisher | : Springer Nature |
Total Pages | : 325 |
Release | : 2020-07-02 |
Genre | : Business & Economics |
ISBN | : 3030427609 |
Download Introduction to the Theory of Nonlinear Optimization Book in PDF, ePub and Kindle
This book serves as an introductory text to optimization theory in normed spaces and covers all areas of nonlinear optimization. It presents fundamentals with particular emphasis on the application to problems in the calculus of variations, approximation and optimal control theory. The reader is expected to have a basic knowledge of linear functional analysis.
Author | : Andrzej Ruszczynski |
Publisher | : Princeton University Press |
Total Pages | : 464 |
Release | : 2011-09-19 |
Genre | : Mathematics |
ISBN | : 1400841054 |
Download Nonlinear Optimization Book in PDF, ePub and Kindle
Optimization is one of the most important areas of modern applied mathematics, with applications in fields from engineering and economics to finance, statistics, management science, and medicine. While many books have addressed its various aspects, Nonlinear Optimization is the first comprehensive treatment that will allow graduate students and researchers to understand its modern ideas, principles, and methods within a reasonable time, but without sacrificing mathematical precision. Andrzej Ruszczynski, a leading expert in the optimization of nonlinear stochastic systems, integrates the theory and the methods of nonlinear optimization in a unified, clear, and mathematically rigorous fashion, with detailed and easy-to-follow proofs illustrated by numerous examples and figures. The book covers convex analysis, the theory of optimality conditions, duality theory, and numerical methods for solving unconstrained and constrained optimization problems. It addresses not only classical material but also modern topics such as optimality conditions and numerical methods for problems involving nondifferentiable functions, semidefinite programming, metric regularity and stability theory of set-constrained systems, and sensitivity analysis of optimization problems. Based on a decade's worth of notes the author compiled in successfully teaching the subject, this book will help readers to understand the mathematical foundations of the modern theory and methods of nonlinear optimization and to analyze new problems, develop optimality theory for them, and choose or construct numerical solution methods. It is a must for anyone seriously interested in optimization.
Author | : Hector O. Fattorini |
Publisher | : Cambridge University Press |
Total Pages | : 828 |
Release | : 1999-03-28 |
Genre | : Computers |
ISBN | : 9780521451253 |
Download Infinite Dimensional Optimization and Control Theory Book in PDF, ePub and Kindle
Treats optimal problems for systems described by ODEs and PDEs, using an approach that unifies finite and infinite dimensional nonlinear programming.
Author | : M. S. Bazaraa |
Publisher | : |
Total Pages | : 193 |
Release | : 1976 |
Genre | : Duality theory (Mathematics) |
ISBN | : 9780387593746 |
Download Foundations of Optimization Book in PDF, ePub and Kindle
Author | : Jiongmin Yong |
Publisher | : World Scientific Publishing Company |
Total Pages | : 236 |
Release | : 2018-05-16 |
Genre | : Mathematics |
ISBN | : 981323766X |
Download Optimization Theory Book in PDF, ePub and Kindle
Author | : Josef Stoer |
Publisher | : |
Total Pages | : 316 |
Release | : 1970 |
Genre | : Convex domains |
ISBN | : |
Download Convexity and Optimization in Finite Dimensions Book in PDF, ePub and Kindle