Modern Nonconvex Nondifferentiable Optimization

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Publisher : SIAM
ISBN 13 : 161197674X
Total Pages : 792 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Modern Nonconvex Nondifferentiable Optimization by : Ying Cui

Download or read book Modern Nonconvex Nondifferentiable Optimization written by Ying Cui and published by SIAM. This book was released on 2021-12-02 with total page 792 pages. Available in PDF, EPUB and Kindle. Book excerpt: Starting with the fundamentals of classical smooth optimization and building on established convex programming techniques, this research monograph presents a foundation and methodology for modern nonconvex nondifferentiable optimization. It provides readers with theory, methods, and applications of nonconvex and nondifferentiable optimization in statistical estimation, operations research, machine learning, and decision making. A comprehensive and rigorous treatment of this emergent mathematical topic is urgently needed in today’s complex world of big data and machine learning. This book takes a thorough approach to the subject and includes examples and exercises to enrich the main themes, making it suitable for classroom instruction. Modern Nonconvex Nondifferentiable Optimization is intended for applied and computational mathematicians, optimizers, operations researchers, statisticians, computer scientists, engineers, economists, and machine learners. It could be used in advanced courses on optimization/operations research and nonconvex and nonsmooth optimization.

Methods of Descent for Nondifferentiable Optimization

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Author :
Publisher : Lecture Notes in Mathematics
ISBN 13 :
Total Pages : 376 pages
Book Rating : 4.0/5 ( download)

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Book Synopsis Methods of Descent for Nondifferentiable Optimization by : Krzysztof C. Kiwiel

Download or read book Methods of Descent for Nondifferentiable Optimization written by Krzysztof C. Kiwiel and published by Lecture Notes in Mathematics. This book was released on 1985-06 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Modern Nonconvex Nondifferentiable Optimization

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Author :
Publisher : Society for Industrial and Applied Mathematics (SIAM)
ISBN 13 : 9781611976731
Total Pages : 0 pages
Book Rating : 4.9/5 (767 download)

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Book Synopsis Modern Nonconvex Nondifferentiable Optimization by : Ying Cui

Download or read book Modern Nonconvex Nondifferentiable Optimization written by Ying Cui and published by Society for Industrial and Applied Mathematics (SIAM). This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This monograph serves present and future needs where nonconvexity and nondifferentiability are inevitably present in the faithful modeling of real-world applications of optimization"--

Global Optimization with Non-Convex Constraints

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Publisher : Springer Science & Business Media
ISBN 13 : 9780792364900
Total Pages : 742 pages
Book Rating : 4.3/5 (649 download)

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Book Synopsis Global Optimization with Non-Convex Constraints by : Roman G. Strongin

Download or read book Global Optimization with Non-Convex Constraints written by Roman G. Strongin and published by Springer Science & Business Media. This book was released on 2000-10-31 with total page 742 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a new approach to global non-convex constrained optimization. Problem dimensionality is reduced via space-filling curves. To economize the search, constraint is accounted separately (penalties are not employed). The multicriteria case is also considered. All techniques are generalized for (non-redundant) execution on multiprocessor systems. Audience: Researchers and students working in optimization, applied mathematics, and computer science.

Progress in Nondifferentiable Optimization

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Publisher :
ISBN 13 :
Total Pages : 272 pages
Book Rating : 4.E/5 ( download)

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Book Synopsis Progress in Nondifferentiable Optimization by : E. A. Nurminski

Download or read book Progress in Nondifferentiable Optimization written by E. A. Nurminski and published by . This book was released on 1982 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Nondifferentiable Optimization

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Publisher : Springer
ISBN 13 : 9781461382683
Total Pages : 0 pages
Book Rating : 4.3/5 (826 download)

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Book Synopsis Nondifferentiable Optimization by : V.F. Dem'yanov

Download or read book Nondifferentiable Optimization written by V.F. Dem'yanov and published by Springer. This book was released on 2012-08-14 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Of recent coinage, the term "nondifferentiable optimization" (NDO) covers a spectrum of problems related to finding extremal values of nondifferentiable functions. Problems of minimizing nonsmooth functions arise in engineering applications as well as in mathematics proper. The Chebyshev approximation problem is an ample illustration of this. Without loss of generality, we shall consider only minimization problems. Among nonsmooth minimization problems, minimax problems and convex problems have been studied extensively ([31], [36], [57], [110], [120]). Interest in NDO has been constantly growing in recent years (monographs: [30], [81], [127] and articles and papers: [14], [20], [87]-[89], [98], [130], [135], [140]-[142], [152], [153], [160], all dealing with various aspects of non smooth optimization). For solving an arbitrary minimization problem, it is neces sary to: 1. Study properties of the objective function, in particular, its differentiability and directional differentiability. 2. Establish necessary (and, if possible, sufficient) condi tions for a global or local minimum. 3. Find the direction of descent (steepest or, simply, feasible--in appropriate sense). 4. Construct methods of successive approximation. In this book, the minimization problems for nonsmooth func tions of a finite number of variables are considered. Of fun damental importance are necessary conditions for an extremum (for example, [24], [45], [57], [73], [74], [103], [159], [163], [167], [168].

Nonsmooth Optimization and Related Topics

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Publisher : Springer Science & Business Media
ISBN 13 : 1475760191
Total Pages : 481 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Nonsmooth Optimization and Related Topics by : F.H. Clarke

Download or read book Nonsmooth Optimization and Related Topics written by F.H. Clarke and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the edited texts of the lect. nres presented at the International School of Mathematics devoted to Nonsmonth Optimization, held from . June 20 to July I, 1988. The site for the meeting was the "Ettore ~Iajorana" Centre for Sci entific Culture in Erice, Sicily. In the tradition of these meetings the main purpose was to give the state-of-the-art of an important and growing field of mathematics, and to stimulate interactions between finite-dimensional and infinite-dimensional op timization. The School was attended by approximately 80 people from 23 countries; in particular it was possible to have some distinguished lecturers from the SO\·iet Union, whose research institutions are here gratt-fnlly acknowledged. Besides the lectures, several seminars were delivered; a special s·~ssion was devoted to numerical computing aspects. The result was a broad exposure. gi ·. ring a deep knowledge of the present research tendencies in the field. We wish to express our appreciation to all the participants. Special mention 5hould be made of the Ettorc ;. . Iajorana Centre in Erice, which helped provide a stimulating and rewarding experience, and of its staff which was fundamental for the success of the meeting. j\, loreover, WP want to extend uur deep appreci

Evaluation Complexity of Algorithms for Nonconvex Optimization

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Publisher : SIAM
ISBN 13 : 1611976995
Total Pages : 549 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Evaluation Complexity of Algorithms for Nonconvex Optimization by : Coralia Cartis

Download or read book Evaluation Complexity of Algorithms for Nonconvex Optimization written by Coralia Cartis and published by SIAM. This book was released on 2022-07-06 with total page 549 pages. Available in PDF, EPUB and Kindle. Book excerpt: A popular way to assess the “effort” needed to solve a problem is to count how many evaluations of the problem functions (and their derivatives) are required. In many cases, this is often the dominating computational cost. Given an optimization problem satisfying reasonable assumptions—and given access to problem-function values and derivatives of various degrees—how many evaluations might be required to approximately solve the problem? Evaluation Complexity of Algorithms for Nonconvex Optimization: Theory, Computation, and Perspectives addresses this question for nonconvex optimization problems, those that may have local minimizers and appear most often in practice. This is the first book on complexity to cover topics such as composite and constrained optimization, derivative-free optimization, subproblem solution, and optimal (lower and sharpness) bounds for nonconvex problems. It is also the first to address the disadvantages of traditional optimality measures and propose useful surrogates leading to algorithms that compute approximate high-order critical points, and to compare traditional and new methods, highlighting the advantages of the latter from a complexity point of view. This is the go-to book for those interested in solving nonconvex optimization problems. It is suitable for advanced undergraduate and graduate students in courses on advanced numerical analysis, data science, numerical optimization, and approximation theory.

Nondifferentiable Optimization

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Publisher :
ISBN 13 :
Total Pages : 488 pages
Book Rating : 4.:/5 (327 download)

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Book Synopsis Nondifferentiable Optimization by : Vladimir Fedorovich Demʹi︠a︡nov

Download or read book Nondifferentiable Optimization written by Vladimir Fedorovich Demʹi︠a︡nov and published by . This book was released on 1985 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Classification and Data Science in the Digital Age

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Publisher : Springer Nature
ISBN 13 : 3031090349
Total Pages : 393 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Classification and Data Science in the Digital Age by : Paula Brito

Download or read book Classification and Data Science in the Digital Age written by Paula Brito and published by Springer Nature. This book was released on 2023-12-07 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: The contributions gathered in this open access book focus on modern methods for data science and classification and present a series of real-world applications. Numerous research topics are covered, ranging from statistical inference and modeling to clustering and dimension reduction, from functional data analysis to time series analysis, and network analysis. The applications reflect new analyses in a variety of fields, including medicine, marketing, genetics, engineering, and education. The book comprises selected and peer-reviewed papers presented at the 17th Conference of the International Federation of Classification Societies (IFCS 2022), held in Porto, Portugal, July 19–23, 2022. The IFCS federates the classification societies and the IFCS biennial conference brings together researchers and stakeholders in the areas of Data Science, Classification, and Machine Learning. It provides a forum for presenting high-quality theoretical and applied works, and promoting and fostering interdisciplinary research and international cooperation. The intended audience is researchers and practitioners who seek the latest developments and applications in the field of data science and classification.

Introduction to Nonlinear Optimization

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Publisher : SIAM
ISBN 13 : 1611977622
Total Pages : 364 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Introduction to Nonlinear Optimization by : Amir Beck

Download or read book Introduction to Nonlinear Optimization written by Amir Beck and published by SIAM. This book was released on 2023-06-29 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: Built on the framework of the successful first edition, this book serves as a modern introduction to the field of optimization. The author’s objective is to provide the foundations of theory and algorithms of nonlinear optimization as well as to present a variety of applications from diverse areas of applied sciences. Introduction to Nonlinear Optimization gradually yet rigorously builds connections between theory, algorithms, applications, and actual implementation. The book contains several topics not typically included in optimization books, such as optimality conditions in sparsity constrained optimization, hidden convexity, and total least squares. Readers will discover a wide array of applications such as circle fitting, Chebyshev center, the Fermat–Weber problem, denoising, clustering, total least squares, and orthogonal regression. These applications are studied both theoretically and algorithmically, illustrating concepts such as duality. Python and MATLAB programs are used to show how the theory can be implemented. The extremely popular CVX toolbox (MATLAB) and CVXPY module (Python) are described and used. More than 250 theoretical, algorithmic, and numerical exercises enhance the reader's understanding of the topics. (More than 70 of the exercises provide detailed solutions, and many others are provided with final answers.) The theoretical and algorithmic topics are illustrated by Python and MATLAB examples. This book is intended for graduate or advanced undergraduate students in mathematics, computer science, electrical engineering, and potentially other engineering disciplines.

Moment and Polynomial Optimization

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Publisher : SIAM
ISBN 13 : 1611977606
Total Pages : 484 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Moment and Polynomial Optimization by : Jiawang Nie

Download or read book Moment and Polynomial Optimization written by Jiawang Nie and published by SIAM. This book was released on 2023-06-15 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: Moment and polynomial optimization is an active research field used to solve difficult questions in many areas, including global optimization, tensor computation, saddle points, Nash equilibrium, and bilevel programs, and it has many applications. The author synthesizes current research and applications, providing a systematic introduction to theory and methods, a comprehensive approach for extracting optimizers and solving truncated moment problems, and a creative methodology for using optimality conditions to construct tight Moment-SOS relaxations. This book is intended for applied mathematicians, engineers, and researchers entering the field. It can be used as a textbook for graduate students in courses on convex optimization, polynomial optimization, and matrix and tensor optimization.

An Introduction to Convexity, Optimization, and Algorithms

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Publisher : SIAM
ISBN 13 : 1611977800
Total Pages : 192 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis An Introduction to Convexity, Optimization, and Algorithms by : Heinz H. Bauschke

Download or read book An Introduction to Convexity, Optimization, and Algorithms written by Heinz H. Bauschke and published by SIAM. This book was released on 2023-12-20 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: This concise, self-contained volume introduces convex analysis and optimization algorithms, with an emphasis on bridging the two areas. It explores cutting-edge algorithms—such as the proximal gradient, Douglas–Rachford, Peaceman–Rachford, and FISTA—that have applications in machine learning, signal processing, image reconstruction, and other fields. An Introduction to Convexity, Optimization, and Algorithms contains algorithms illustrated by Julia examples and more than 200 exercises that enhance the reader’s understanding of the topic. Clear explanations and step-by-step algorithmic descriptions facilitate self-study for individuals looking to enhance their expertise in convex analysis and optimization. Designed for courses in convex analysis, numerical optimization, and related subjects, this volume is intended for undergraduate and graduate students in mathematics, computer science, and engineering. Its concise length makes it ideal for a one-semester course. Researchers and professionals in applied areas, such as data science and machine learning, will find insights relevant to their work.

Problems and Solutions for Integer and Combinatorial Optimization

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Publisher : SIAM
ISBN 13 : 1611977762
Total Pages : 148 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Problems and Solutions for Integer and Combinatorial Optimization by : Mustafa Ç. Pınar

Download or read book Problems and Solutions for Integer and Combinatorial Optimization written by Mustafa Ç. Pınar and published by SIAM. This book was released on 2023-11-10 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: The only book offering solved exercises for integer and combinatorial optimization, this book contains 102 classroom tested problems of varying scope and difficulty chosen from a plethora of topics and applications. It has an associated website containing additional problems, lecture notes, and suggested readings. Topics covered include modeling capabilities of integer variables, the Branch-and-Bound method, cutting planes, network optimization models, shortest path problems, optimum tree problems, maximal cardinality matching problems, matching-covering duality, symmetric and asymmetric TSP, 2-matching and 1-tree relaxations, VRP formulations, and dynamic programming. Problems and Solutions for Integer and Combinatorial Optimization: Building Skills in Discrete Optimization is meant for undergraduate and beginning graduate students in mathematics, computer science, and engineering to use for self-study and for instructors to use in conjunction with other course material and when teaching courses in discrete optimization.

Second-Order Variational Analysis in Optimization, Variational Stability, and Control

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Publisher : Springer Nature
ISBN 13 : 303153476X
Total Pages : 802 pages
Book Rating : 4.0/5 (315 download)

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Book Synopsis Second-Order Variational Analysis in Optimization, Variational Stability, and Control by : Boris S. Mordukhovich

Download or read book Second-Order Variational Analysis in Optimization, Variational Stability, and Control written by Boris S. Mordukhovich and published by Springer Nature. This book was released on with total page 802 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Large-Scale Nonlinear Optimization

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Publisher : Springer Science & Business Media
ISBN 13 : 0387300651
Total Pages : 297 pages
Book Rating : 4.3/5 (873 download)

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Book Synopsis Large-Scale Nonlinear Optimization by : Gianni Pillo

Download or read book Large-Scale Nonlinear Optimization written by Gianni Pillo and published by Springer Science & Business Media. This book was released on 2006-06-03 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Nondifferentiable Optimization

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Publisher :
ISBN 13 : 9780720483000
Total Pages : 0 pages
Book Rating : 4.4/5 (83 download)

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Book Synopsis Nondifferentiable Optimization by : Michel Louis Balinski

Download or read book Nondifferentiable Optimization written by Michel Louis Balinski and published by . This book was released on 1975 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: