Evaluation Complexity Of Algorithms For Nonconvex Optimization

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Evaluation Complexity of Algorithms for Nonconvex Optimization

Author : Coralia Cartis
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.

Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes)

Author : Boyan Sirakov
Publisher : World Scientific
ISBN 13 : 9813272899
Total Pages : 5393 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes) by : Boyan Sirakov

Download or read book Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes) written by Boyan Sirakov and published by World Scientific. This book was released on 2019-02-27 with total page 5393 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios.

Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging

Author : Ke Chen
Publisher : Springer Nature
ISBN 13 : 3030986616
Total Pages : 1981 pages
Book Rating : 4.0/5 (39 download)

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Book Synopsis Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging by : Ke Chen

Download or read book Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging written by Ke Chen and published by Springer Nature. This book was released on 2023-02-24 with total page 1981 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook gathers together the state of the art on mathematical models and algorithms for imaging and vision. Its emphasis lies on rigorous mathematical methods, which represent the optimal solutions to a class of imaging and vision problems, and on effective algorithms, which are necessary for the methods to be translated to practical use in various applications. Viewing discrete images as data sampled from functional surfaces enables the use of advanced tools from calculus, functions and calculus of variations, and nonlinear optimization, and provides the basis of high-resolution imaging through geometry and variational models. Besides, optimization naturally connects traditional model-driven approaches to the emerging data-driven approaches of machine and deep learning. No other framework can provide comparable accuracy and precision to imaging and vision. Written by leading researchers in imaging and vision, the chapters in this handbook all start with gentle introductions, which make this work accessible to graduate students. For newcomers to the field, the book provides a comprehensive and fast-track introduction to the content, to save time and get on with tackling new and emerging challenges. For researchers, exposure to the state of the art of research works leads to an overall view of the entire field so as to guide new research directions and avoid pitfalls in moving the field forward and looking into the next decades of imaging and information services. This work can greatly benefit graduate students, researchers, and practitioners in imaging and vision; applied mathematicians; medical imagers; engineers; and computer scientists.

An Introduction to Convexity, Optimization, and Algorithms

Author : Heinz H. Bauschke
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.

Approximation and Optimization

Author : Ioannis C. Demetriou
Publisher : Springer
ISBN 13 : 3030127672
Total Pages : 244 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Approximation and Optimization by : Ioannis C. Demetriou

Download or read book Approximation and Optimization written by Ioannis C. Demetriou and published by Springer. This book was released on 2019-05-10 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on the development of approximation-related algorithms and their relevant applications. Individual contributions are written by leading experts and reflect emerging directions and connections in data approximation and optimization. Chapters discuss state of the art topics with highly relevant applications throughout science, engineering, technology and social sciences. Academics, researchers, data science practitioners, business analysts, social sciences investigators and graduate students will find the number of illustrations, applications, and examples provided useful. This volume is based on the conference Approximation and Optimization: Algorithms, Complexity, and Applications, which was held in the National and Kapodistrian University of Athens, Greece, June 29–30, 2017. The mix of survey and research content includes topics in approximations to discrete noisy data; binary sequences; design of networks and energy systems; fuzzy control; large scale optimization; noisy data; data-dependent approximation; networked control systems; machine learning ; optimal design; no free lunch theorem; non-linearly constrained optimization; spectroscopy.

Introduction to Nonlinear Optimization

Author : Amir Beck
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.

Problems and Solutions for Integer and Combinatorial Optimization

Author : Mustafa Ç. Pınar
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.

Moment and Polynomial Optimization

Author : Jiawang Nie
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.

Trust Region Methods

Author : A. R. Conn
Publisher : SIAM
ISBN 13 : 0898714605
Total Pages : 960 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Trust Region Methods by : A. R. Conn

Download or read book Trust Region Methods written by A. R. Conn and published by SIAM. This book was released on 2000-01-01 with total page 960 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- General.

Machine Learning, Optimization, and Big Data

Author : Giuseppe Nicosia
Publisher : Springer
ISBN 13 : 3319729268
Total Pages : 621 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Machine Learning, Optimization, and Big Data by : Giuseppe Nicosia

Download or read book Machine Learning, Optimization, and Big Data written by Giuseppe Nicosia and published by Springer. This book was released on 2017-12-19 with total page 621 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the post-conference proceedings of the Third International Workshop on Machine Learning, Optimization, and Big Data, MOD 2017, held in Volterra, Italy, in September 2017. The 50 full papers presented were carefully reviewed and selected from 126 submissions. The papers cover topics in the field of machine learning, artificial intelligence, computational optimization and data science presenting a substantial array of ideas, technologies, algorithms, methods and applications.

High-Dimensional Optimization and Probability

Author : Ashkan Nikeghbali
Publisher : Springer Nature
ISBN 13 : 3031008324
Total Pages : 417 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis High-Dimensional Optimization and Probability by : Ashkan Nikeghbali

Download or read book High-Dimensional Optimization and Probability written by Ashkan Nikeghbali and published by Springer Nature. This book was released on 2022-08-04 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents extensive research devoted to a broad spectrum of mathematics with emphasis on interdisciplinary aspects of Optimization and Probability. Chapters also emphasize applications to Data Science, a timely field with a high impact in our modern society. The discussion presents modern, state-of-the-art, research results and advances in areas including non-convex optimization, decentralized distributed convex optimization, topics on surrogate-based reduced dimension global optimization in process systems engineering, the projection of a point onto a convex set, optimal sampling for learning sparse approximations in high dimensions, the split feasibility problem, higher order embeddings, codifferentials and quasidifferentials of the expectation of nonsmooth random integrands, adjoint circuit chains associated with a random walk, analysis of the trade-off between sample size and precision in truncated ordinary least squares, spatial deep learning, efficient location-based tracking for IoT devices using compressive sensing and machine learning techniques, and nonsmooth mathematical programs with vanishing constraints in Banach spaces. The book is a valuable source for graduate students as well as researchers working on Optimization, Probability and their various interconnections with a variety of other areas. Chapter 12 is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.

Global Optimization with Non-Convex Constraints

Author : Roman G. Strongin
Publisher : Springer Science & Business Media
ISBN 13 : 146154677X
Total Pages : 717 pages
Book Rating : 4.4/5 (615 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 2013-11-09 with total page 717 pages. Available in PDF, EPUB and Kindle. Book excerpt: Everything should be made as simple as possible, but not simpler. (Albert Einstein, Readers Digest, 1977) The modern practice of creating technical systems and technological processes of high effi.ciency besides the employment of new principles, new materials, new physical effects and other new solutions ( which is very traditional and plays the key role in the selection of the general structure of the object to be designed) also includes the choice of the best combination for the set of parameters (geometrical sizes, electrical and strength characteristics, etc.) concretizing this general structure, because the Variation of these parameters ( with the structure or linkage being already set defined) can essentially affect the objective performance indexes. The mathematical tools for choosing these best combinations are exactly what is this book about. With the advent of computers and the computer-aided design the pro bations of the selected variants are usually performed not for the real examples ( this may require some very expensive building of sample op tions and of the special installations to test them ), but by the analysis of the corresponding mathematical models. The sophistication of the mathematical models for the objects to be designed, which is the natu ral consequence of the raising complexity of these objects, greatly com plicates the objective performance analysis. Today, the main (and very often the only) available instrument for such an analysis is computer aided simulation of an object's behavior, based on numerical experiments with its mathematical model.

Global Optimization

Author : Marco Locatelli
Publisher : SIAM
ISBN 13 : 1611972671
Total Pages : 439 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Global Optimization by : Marco Locatelli

Download or read book Global Optimization written by Marco Locatelli and published by SIAM. This book was released on 2013-10-16 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a thorough overview of the rapidly growing field of global optimization, with chapters on key topics such as complexity, heuristic methods, derivation of lower bounds for minimization problems, and branch-and-bound methods and convergence. The final chapter offers both benchmark test problems and applications of global optimization, such as finding the conformation of a molecule or planning an optimal trajectory for interplanetary space travel. An appendix provides fundamental information on convex and concave functions. Intended for Ph.D. students, researchers, and practitioners looking for advanced solution methods to difficult optimization problems. It can be used as a supplementary text in an advanced graduate-level seminar.

Algorithms for Optimization

Author : Mykel J. Kochenderfer
Publisher : MIT Press
ISBN 13 : 0262039427
Total Pages : 521 pages
Book Rating : 4.2/5 (62 download)

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Book Synopsis Algorithms for Optimization by : Mykel J. Kochenderfer

Download or read book Algorithms for Optimization written by Mykel J. Kochenderfer and published by MIT Press. This book was released on 2019-03-12 with total page 521 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive introduction to optimization with a focus on practical algorithms for the design of engineering systems. This book offers a comprehensive introduction to optimization with a focus on practical algorithms. The book approaches optimization from an engineering perspective, where the objective is to design a system that optimizes a set of metrics subject to constraints. Readers will learn about computational approaches for a range of challenges, including searching high-dimensional spaces, handling problems where there are multiple competing objectives, and accommodating uncertainty in the metrics. Figures, examples, and exercises convey the intuition behind the mathematical approaches. The text provides concrete implementations in the Julia programming language. Topics covered include derivatives and their generalization to multiple dimensions; local descent and first- and second-order methods that inform local descent; stochastic methods, which introduce randomness into the optimization process; linear constrained optimization, when both the objective function and the constraints are linear; surrogate models, probabilistic surrogate models, and using probabilistic surrogate models to guide optimization; optimization under uncertainty; uncertainty propagation; expression optimization; and multidisciplinary design optimization. Appendixes offer an introduction to the Julia language, test functions for evaluating algorithm performance, and mathematical concepts used in the derivation and analysis of the optimization methods discussed in the text. The book can be used by advanced undergraduates and graduate students in mathematics, statistics, computer science, any engineering field, (including electrical engineering and aerospace engineering), and operations research, and as a reference for professionals.

First-order and Stochastic Optimization Methods for Machine Learning

Author : Guanghui Lan
Publisher : Springer Nature
ISBN 13 : 3030395685
Total Pages : 591 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis First-order and Stochastic Optimization Methods for Machine Learning by : Guanghui Lan

Download or read book First-order and Stochastic Optimization Methods for Machine Learning written by Guanghui Lan and published by Springer Nature. This book was released on 2020-05-15 with total page 591 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers not only foundational materials but also the most recent progresses made during the past few years on the area of machine learning algorithms. In spite of the intensive research and development in this area, there does not exist a systematic treatment to introduce the fundamental concepts and recent progresses on machine learning algorithms, especially on those based on stochastic optimization methods, randomized algorithms, nonconvex optimization, distributed and online learning, and projection free methods. This book will benefit the broad audience in the area of machine learning, artificial intelligence and mathematical programming community by presenting these recent developments in a tutorial style, starting from the basic building blocks to the most carefully designed and complicated algorithms for machine learning.

Lectures on Convex Optimization

Author : Yurii Nesterov
Publisher : Springer
ISBN 13 : 3319915789
Total Pages : 603 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Lectures on Convex Optimization by : Yurii Nesterov

Download or read book Lectures on Convex Optimization written by Yurii Nesterov and published by Springer. This book was released on 2018-11-19 with total page 603 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive, modern introduction to convex optimization, a field that is becoming increasingly important in applied mathematics, economics and finance, engineering, and computer science, notably in data science and machine learning. Written by a leading expert in the field, this book includes recent advances in the algorithmic theory of convex optimization, naturally complementing the existing literature. It contains a unified and rigorous presentation of the acceleration techniques for minimization schemes of first- and second-order. It provides readers with a full treatment of the smoothing technique, which has tremendously extended the abilities of gradient-type methods. Several powerful approaches in structural optimization, including optimization in relative scale and polynomial-time interior-point methods, are also discussed in detail. Researchers in theoretical optimization as well as professionals working on optimization problems will find this book very useful. It presents many successful examples of how to develop very fast specialized minimization algorithms. Based on the author’s lectures, it can naturally serve as the basis for introductory and advanced courses in convex optimization for students in engineering, economics, computer science and mathematics.

Numerical Analysis and Optimization

Author : Mehiddin Al-Baali
Publisher : Springer Nature
ISBN 13 : 3030720403
Total Pages : 307 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis Numerical Analysis and Optimization by : Mehiddin Al-Baali

Download or read book Numerical Analysis and Optimization written by Mehiddin Al-Baali and published by Springer Nature. This book was released on 2021-12-01 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gathers selected, peer-reviewed contributions presented at the Fifth International Conference on Numerical Analysis and Optimization (NAO-V), which was held at Sultan Qaboos University, Oman, on January 6-9, 2020. Each chapter reports on developments in key fields, such as numerical analysis, numerical optimization, numerical linear algebra, numerical differential equations, optimal control, approximation theory, applied mathematics, derivative-free optimization methods, programming models, and challenging applications that frequently arise in statistics, econometrics, finance, physics, medicine, biology, engineering and industry. Many real-world, complex problems can be formulated as optimization tasks, and can be characterized further as large scale, unconstrained, constrained, non-convex, nondifferentiable or discontinuous, and therefore require adequate computational methods, algorithms and software tools. These same tools are often employed by researchers working in current IT hot topics, such as big data, optimization and other complex numerical algorithms in the cloud, devising special techniques for supercomputing systems. This interdisciplinary view permeates the work included in this volume. The NAO conference series is held every three years at Sultan Qaboos University, with the aim of bringing together a group of international experts and presenting novel and advanced applications to facilitate interdisciplinary studies among pure scientific and applied knowledge. It is a venue where prominent scientists gather to share innovative ideas and know-how relating to new scientific methodologies, to promote scientific exchange, to discuss possible future cooperations, and to promote the mobility of local and young researchers.