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| Author | : Francisco J. Aragón |
| Publisher | : Springer |
| Total Pages | : 350 |
| Release | : 2019-02-27 |
| Genre | : Mathematics |
| ISBN | : 3030111849 |
Download Nonlinear Optimization Book in PDF, ePub and Kindle
This textbook on nonlinear optimization focuses on model building, real world problems, and applications of optimization models to natural and social sciences. Organized into two parts, this book may be used as a primary text for courses on convex optimization and non-convex optimization. Definitions, proofs, and numerical methods are well illustrated and all chapters contain compelling exercises. The exercises emphasize fundamental theoretical results on optimality and duality theorems, numerical methods with or without constraints, and derivative-free optimization. Selected solutions are given. Applications to theoretical results and numerical methods are highlighted to help students comprehend methods and techniques.
| 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 | : Amir Beck |
| Publisher | : SIAM |
| Total Pages | : 282 |
| Release | : 2014-10-27 |
| Genre | : Mathematics |
| ISBN | : 1611973651 |
Download Introduction to Nonlinear Optimization Book in PDF, ePub and Kindle
This book provides the foundations of the theory of nonlinear optimization as well as some related algorithms and presents a variety of applications from diverse areas of applied sciences. The author combines three pillars of optimization?theoretical and algorithmic foundation, familiarity with various applications, and the ability to apply the theory and algorithms on actual problems?and rigorously and gradually builds the connection between theory, algorithms, applications, and implementation. Readers will find more than 170 theoretical, algorithmic, and numerical exercises that deepen and enhance the reader's understanding of the topics. The author includes offers several subjects not typically found in optimization books?for example, optimality conditions in sparsity-constrained optimization, hidden convexity, and total least squares. The book also offers a large number of applications discussed theoretically and algorithmically, such as circle fitting, Chebyshev center, the Fermat?Weber problem, denoising, clustering, total least squares, and orthogonal regression and theoretical and algorithmic topics demonstrated by the MATLAB? toolbox CVX and a package of m-files that is posted on the book?s web site.
| 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 | : H. A. Eiselt |
| Publisher | : Springer Nature |
| Total Pages | : 366 |
| Release | : 2019-11-09 |
| Genre | : Mathematics |
| ISBN | : 3030194620 |
Download Nonlinear Optimization Book in PDF, ePub and Kindle
This book provides a comprehensive introduction to nonlinear programming, featuring a broad range of applications and solution methods in the field of continuous optimization. It begins with a summary of classical results on unconstrained optimization, followed by a wealth of applications from a diverse mix of fields, e.g. location analysis, traffic planning, and water quality management, to name but a few. In turn, the book presents a formal description of optimality conditions, followed by an in-depth discussion of the main solution techniques. Each method is formally described, and then fully solved using a numerical example.
| Author | : Michael Bartholomew-Biggs |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 296 |
| Release | : 2008-12-16 |
| Genre | : Mathematics |
| ISBN | : 0387787232 |
Download Nonlinear Optimization with Engineering Applications Book in PDF, ePub and Kindle
This textbook examines a broad range of problems in science and engineering, describing key numerical methods applied to real life. The case studies presented are in such areas as data fitting, vehicle route planning and optimal control, scheduling and resource allocation, sensitivity calculations and worst-case analysis. Chapters are self-contained with exercises provided at the end of most sections. Nonlinear Optimization with Engineering Applications is ideal for self-study and classroom use in engineering courses at the senior undergraduate or graduate level. The book will also appeal to postdocs and advanced researchers interested in the development and use of optimization algorithms.
| 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 | : Neculai Andrei |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 356 |
| Release | : 2013-06-22 |
| Genre | : Mathematics |
| ISBN | : 1461467977 |
Download Nonlinear Optimization Applications Using the GAMS Technology Book in PDF, ePub and Kindle
Here is a collection of nonlinear optimization applications from the real world, expressed in the General Algebraic Modeling System (GAMS). The concepts are presented so that the reader can quickly modify and update them to represent real-world situations.
| Author | : Gianni Pillo |
| Publisher | : Springer |
| Total Pages | : 0 |
| Release | : 2011-02-11 |
| Genre | : Mathematics |
| ISBN | : 9781441940148 |
Download Large-Scale Nonlinear Optimization Book in PDF, ePub and Kindle
This book reviews and discusses recent advances in the development of methods and algorithms for nonlinear optimization and its applications, focusing on the large-dimensional case, the current forefront of much research. Individual chapters, contributed by eminent authorities, provide an up-to-date overview of the field from different and complementary standpoints, including theoretical analysis, algorithmic development, implementation issues and applications.
| Author | : Igor Griva |
| Publisher | : SIAM |
| Total Pages | : 742 |
| Release | : 2009-03-26 |
| Genre | : Mathematics |
| ISBN | : 0898716616 |
Download Linear and Nonlinear Optimization Book in PDF, ePub and Kindle
Flexible graduate textbook that introduces the applications, theory, and algorithms of linear and nonlinear optimization in a clear succinct style, supported by numerous examples and exercises. It introduces important realistic applications and explains how optimization can address them.
