Anintroduction To Continuous Optimization Second Edition

Author : Roman A. Polyak
Publisher : Springer Nature
ISBN 13 : 3030687139
Total Pages : 552 pages
Book Rating : 4.37/5 ( download)

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Download or read book Introduction to Continuous Optimization written by Roman A. Polyak and published by Springer Nature. This book was released on 2021-04-29 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained monograph presents the reader with an authoritative view of Continuous Optimization, an area of mathematical optimization that has experienced major developments during the past 40 years. The book contains results which have not yet been covered in a systematic way as well as a summary of results on NR theory and methods developed over the last several decades. The readership is aimed to graduate students in applied mathematics, computer science, economics, as well as researchers working in optimization and those applying optimization methods for solving real life problems. Sufficient exercises throughout provide graduate students and instructors with practical utility in a two-semester course in Continuous Optimization. The topical coverage includes interior point methods, self-concordance theory and related complexity issues, first and second order methods with accelerated convergence, nonlinear rescaling (NR) theory and exterior point methods, just to mention a few. The book contains a unified approach to both interior and exterior point methods with emphasis of the crucial duality role. One of the main achievements of the book shows what makes the exterior point methods numerically attractive and why. The book is composed in five parts. The first part contains the basics of calculus, convex analysis, elements of unconstrained optimization, as well as classical results of linear and convex optimization. The second part contains the basics of self-concordance theory and interior point methods, including complexity results for LP, QP, and QP with quadratic constraint, semidefinite and conic programming. In the third part, the NR and Lagrangian transformation theories are considered and exterior point methods are described. Three important problems in finding equilibrium are considered in the fourth part. In the fifth and final part of the book, several important applications arising in economics, structural optimization, medicine, statistical learning theory, and more, are detailed. Numerical results, obtained by solving a number of real life and test problems, are also provided.

Author : Niclas Andreasson
Publisher : Courier Dover Publications
ISBN 13 : 0486802876
Total Pages : 515 pages
Book Rating : 4.79/5 ( download)

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Download or read book An Introduction to Continuous Optimization written by Niclas Andreasson and published by Courier Dover Publications. This book was released on 2020-01-15 with total page 515 pages. Available in PDF, EPUB and Kindle. Book excerpt: This treatment focuses on the analysis and algebra underlying the workings of convexity and duality and necessary/sufficient local/global optimality conditions for unconstrained and constrained optimization problems. 2015 edition.

Author : Morton I. Kamien
Publisher : Courier Corporation
ISBN 13 : 0486310280
Total Pages : 402 pages
Book Rating : 4.82/5 ( download)

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Download or read book Dynamic Optimization, Second Edition written by Morton I. Kamien and published by Courier Corporation. This book was released on 2013-04-17 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since its initial publication, this text has defined courses in dynamic optimization taught to economics and management science students. The two-part treatment covers the calculus of variations and optimal control. 1998 edition.

Author : Niclas Andréasson
Publisher :
ISBN 13 : 9789144115290
Total Pages : pages
Book Rating : 4.96/5 ( download)

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Download or read book An Introduction to Continuous Optimization written by Niclas Andréasson and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Jorge Nocedal
Publisher : Springer Science & Business Media
ISBN 13 : 0387400656
Total Pages : 686 pages
Book Rating : 4.55/5 ( download)

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Download or read book Numerical Optimization written by Jorge Nocedal and published by Springer Science & Business Media. This book was released on 2006-12-11 with total page 686 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimization is an important tool used in decision science and for the analysis of physical systems used in engineering. One can trace its roots to the Calculus of Variations and the work of Euler and Lagrange. This natural and reasonable approach to mathematical programming covers numerical methods for finite-dimensional optimization problems. It begins with very simple ideas progressing through more complicated concepts, concentrating on methods for both unconstrained and constrained optimization.

Author : Niclas Andreasson
Publisher : Studentlitteratur AB
ISBN 13 : 9789144060774
Total Pages : 484 pages
Book Rating : 4.77/5 ( download)

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Download or read book Anintroduction to Continuous Optimization / Second Edition written by Niclas Andreasson and published by Studentlitteratur AB. This book was released on 2013-10-01 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimisation, or mathematical programming, is a fundamental subject within decision science and operations research, in which mathematical decision models are constructed, analysed, and solved. The books focus lies on providing a basis for the analysis of optimisation models and of candidate optimal solutions for continuous optimisation models. The main part of the mathematical material therefore concerns the analysis and linear algebra that underlie the workings of convexity and duality, and necessary/sufficient local/global optimality conditions for continuous optimisation problems. Natural algorithms are then developed from these optimality conditions, and their most important convergence characteristics are analysed. The book answers many more questions of the form Why? and Why not? than How?. We use only elementary mathematics in the development of the book, yet are rigorous throughout. The book provides lecture, exercise and reading material for a first course on continuous optimisation and mathematical programming, geared towards third-year students, and has already been used as such for nearly ten years. The preface to the second edition describes the main changes made since the first, 2005, edition. The book can be used in mathematical optimisation courses at any mathematics, engineering, economics, and business schools. It is a perfect starting book for anyone who wishes to develop his/her understanding of the subject of optimisation, before actually applying it.

Author : Mohit Tawarmalani
Publisher : Springer Science & Business Media
ISBN 13 : 1475735324
Total Pages : 492 pages
Book Rating : 4.21/5 ( download)

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Download or read book Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming written by Mohit Tawarmalani and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: Interest in constrained optimization originated with the simple linear pro gramming model since it was practical and perhaps the only computationally tractable model at the time. Constrained linear optimization models were soon adopted in numerous application areas and are perhaps the most widely used mathematical models in operations research and management science at the time of this writing. Modelers have, however, found the assumption of linearity to be overly restrictive in expressing the real-world phenomena and problems in economics, finance, business, communication, engineering design, computational biology, and other areas that frequently demand the use of nonlinear expressions and discrete variables in optimization models. Both of these extensions of the linear programming model are NP-hard, thus representing very challenging problems. On the brighter side, recent advances in algorithmic and computing technology make it possible to re visit these problems with the hope of solving practically relevant problems in reasonable amounts of computational time. Initial attempts at solving nonlinear programs concentrated on the de velopment of local optimization methods guaranteeing globality under the assumption of convexity. On the other hand, the integer programming liter ature has concentrated on the development of methods that ensure global optima. The aim of this book is to marry the advancements in solving nonlinear and integer programming models and to develop new results in the more general framework of mixed-integer nonlinear programs (MINLPs) with the goal of devising practically efficient global optimization algorithms for MINLPs.

Author : Amir Beck
Publisher : SIAM
ISBN 13 : 1611973651
Total Pages : 282 pages
Book Rating : 4.55/5 ( download)

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Download or read book Introduction to Nonlinear Optimization written by Amir Beck and published by SIAM. This book was released on 2014-10-27 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
ISBN 13 : 0387312560
Total Pages : 316 pages
Book Rating : 4.69/5 ( download)

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Download or read book Convex Analysis and Nonlinear Optimization written by Jonathan Borwein and published by Springer Science & Business Media. This book was released on 2010-05-05 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Michel C. Delfour
Publisher : SIAM
ISBN 13 : 1611975964
Total Pages : 445 pages
Book Rating : 4.63/5 ( download)

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Download or read book Introduction to Optimization and Hadamard Semidifferential Calculus, Second Edition written by Michel C. Delfour and published by SIAM. This book was released on 2019-12-19 with total page 445 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second edition provides an enhanced exposition of the long-overlooked Hadamard semidifferential calculus, first introduced in the 1920s by mathematicians Jacques Hadamard and Maurice René Fréchet. Hadamard semidifferential calculus is possibly the largest family of nondifferentiable functions that retains all the features of classical differential calculus, including the chain rule, making it a natural framework for initiating a large audience of undergraduates and non-mathematicians into the world of nondifferentiable optimization. Introduction to Optimization and Hadamard Semidifferential Calculus, Second Edition builds upon its prior edition’s foundations in Hadamard semidifferential calculus, showcasing new material linked to convex analysis and nonsmooth optimization. It presents a modern treatment of optimization and Hadamard semidifferential calculus while remaining at a level that is accessible to undergraduate students, and challenges students with exercises related to problems in such fields as engineering, mechanics, medicine, physics, and economics. Answers are supplied in Appendix B. Students of mathematics, physics, engineering, economics, and other disciplines that demand a basic knowledge of mathematical analysis and linear algebra will find this a fitting primary or companion resource for their studies. This textbook has been designed and tested for a one-term course at the undergraduate level. In its full version, it is appropriate for a first-year graduate course and as a reference.