Evaluation Complexity Of Algorithms For Nonconvex Optimization

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Evaluation Complexity of Algorithms for Nonconvex Optimization

Coralia Cartis,Nicholas I. M. Gould,Philippe L. Toint
Evaluation Complexity of Algorithms for Nonconvex Optimization Book PDF

Author : Coralia Cartis,Nicholas I. M. Gould,Philippe L. Toint
Publisher : SIAM
Page : 549 pages
File Size : 50,8 Mb
Release : 2022-07-06
Category : Mathematics
ISBN : 9781611976991

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Evaluation Complexity of Algorithms for Nonconvex Optimization by Coralia Cartis,Nicholas I. M. Gould,Philippe L. Toint Pdf

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.

Conjugate Gradient Algorithms in Nonconvex Optimization

Radoslaw Pytlak
Conjugate Gradient Algorithms in Nonconvex Optimization Book PDF

Author : Radoslaw Pytlak
Publisher : Springer Science & Business Media
Page : 493 pages
File Size : 52,8 Mb
Release : 2008-11-18
Category : Mathematics
ISBN : 9783540856344

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Conjugate Gradient Algorithms in Nonconvex Optimization by Radoslaw Pytlak Pdf

This book details algorithms for large-scale unconstrained and bound constrained optimization. It shows optimization techniques from a conjugate gradient algorithm perspective as well as methods of shortest residuals, which have been developed by the author.

Global Optimization with Non-Convex Constraints

Roman G. Strongin,Yaroslav D. Sergeyev
Global Optimization with Non Convex Constraints Book PDF

Author : Roman G. Strongin,Yaroslav D. Sergeyev
Publisher : Springer Science & Business Media
Page : 717 pages
File Size : 42,6 Mb
Release : 2013-11-09
Category : Mathematics
ISBN : 9781461546771

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Global Optimization with Non-Convex Constraints by Roman G. Strongin,Yaroslav D. Sergeyev Pdf

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.

An Introduction to Convexity, Optimization, and Algorithms

Heinz H. Bauschke,Walaa M. Moursi
An Introduction to Convexity Optimization and Algorithms Book PDF

Author : Heinz H. Bauschke,Walaa M. Moursi
Publisher : SIAM
Page : 192 pages
File Size : 50,5 Mb
Release : 2023-12-20
Category : Mathematics
ISBN : 9781611977806

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An Introduction to Convexity, Optimization, and Algorithms by Heinz H. Bauschke,Walaa M. Moursi Pdf

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.

Introduction to Nonlinear Optimization

Amir Beck
Introduction to Nonlinear Optimization Book PDF

Author : Amir Beck
Publisher : SIAM
Page : 364 pages
File Size : 46,7 Mb
Release : 2023-06-29
Category : Mathematics
ISBN : 9781611977622

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Introduction to Nonlinear Optimization by Amir Beck Pdf

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

Mustafa Ç. Pınar,Deniz Akkaya
Problems and Solutions for Integer and Combinatorial Optimization Book PDF

Author : Mustafa Ç. Pınar,Deniz Akkaya
Publisher : SIAM
Page : 148 pages
File Size : 44,6 Mb
Release : 2023-11-10
Category : Mathematics
ISBN : 9781611977769

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Problems and Solutions for Integer and Combinatorial Optimization by Mustafa Ç. Pınar,Deniz Akkaya Pdf

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

Jiawang Nie
Moment and Polynomial Optimization Book PDF

Author : Jiawang Nie
Publisher : SIAM
Page : 484 pages
File Size : 55,7 Mb
Release : 2023-06-15
Category : Mathematics
ISBN : 9781611977608

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Moment and Polynomial Optimization by Jiawang Nie Pdf

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.

Non-Convex Multi-Objective Optimization

Panos M. Pardalos,Antanas Žilinskas,Julius Žilinskas
Non Convex Multi Objective Optimization Book PDF

Author : Panos M. Pardalos,Antanas Žilinskas,Julius Žilinskas
Publisher : Springer
Page : 196 pages
File Size : 41,8 Mb
Release : 2017-07-27
Category : Mathematics
ISBN : 9783319610078

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Non-Convex Multi-Objective Optimization by Panos M. Pardalos,Antanas Žilinskas,Julius Žilinskas Pdf

Recent results on non-convex multi-objective optimization problems and methods are presented in this book, with particular attention to expensive black-box objective functions. Multi-objective optimization methods facilitate designers, engineers, and researchers to make decisions on appropriate trade-offs between various conflicting goals. A variety of deterministic and stochastic multi-objective optimization methods are developed in this book. Beginning with basic concepts and a review of non-convex single-objective optimization problems; this book moves on to cover multi-objective branch and bound algorithms, worst-case optimal algorithms (for Lipschitz functions and bi-objective problems), statistical models based algorithms, and probabilistic branch and bound approach. Detailed descriptions of new algorithms for non-convex multi-objective optimization, their theoretical substantiation, and examples for practical applications to the cell formation problem in manufacturing engineering, the process design in chemical engineering, and business process management are included to aide researchers and graduate students in mathematics, computer science, engineering, economics, and business management.

Machine Learning, Optimization, and Big Data

Giuseppe Nicosia,Panos Pardalos,Giovanni Giuffrida,Renato Umeton
Machine Learning Optimization and Big Data Book PDF

Author : Giuseppe Nicosia,Panos Pardalos,Giovanni Giuffrida,Renato Umeton
Publisher : Springer
Page : 621 pages
File Size : 46,9 Mb
Release : 2017-12-19
Category : Computers
ISBN : 9783319729268

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Machine Learning, Optimization, and Big Data by Giuseppe Nicosia,Panos Pardalos,Giovanni Giuffrida,Renato Umeton Pdf

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.

Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging

Ke Chen,Carola-Bibiane Schönlieb,Xue-Cheng Tai,Laurent Younes
Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging Book PDF

Author : Ke Chen,Carola-Bibiane Schönlieb,Xue-Cheng Tai,Laurent Younes
Publisher : Springer Nature
Page : 1981 pages
File Size : 46,7 Mb
Release : 2023-02-24
Category : Mathematics
ISBN : 9783030986612

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Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging by Ke Chen,Carola-Bibiane Schönlieb,Xue-Cheng Tai,Laurent Younes Pdf

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.

Approximation and Optimization

Ioannis C. Demetriou,Panos M. Pardalos
Approximation and Optimization Book PDF

Author : Ioannis C. Demetriou,Panos M. Pardalos
Publisher : Springer
Page : 237 pages
File Size : 52,6 Mb
Release : 2019-05-10
Category : Mathematics
ISBN : 9783030127671

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Approximation and Optimization by Ioannis C. Demetriou,Panos M. Pardalos Pdf

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.

Nonlinear Optimization

Stephen A. Vavasis
Nonlinear Optimization Book PDF

Author : Stephen A. Vavasis
Publisher : Oxford University Press, USA
Page : 192 pages
File Size : 42,6 Mb
Release : 1991
Category : Computers
ISBN : UOM:39015024818406

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Nonlinear Optimization by Stephen A. Vavasis Pdf

The fields of computer science and optimization greatly influence each other, and this book is about one important connection between the two: complexity theory. Complexity theory underlies computer algorithms and is used to address such questions as the efficiency of algorithms and the possibility of algorithmic solutions for particular problems. Furthermore, as optimization problems increase in size with hardware capacity, complexity theory plays a steadily growing role in the exploration of optimization algorithms. As larger and more complicated problems are addressed, it is more important than ever to understand the asymptotic complexity issues. This book describes some of the key developments in the complexity aspects of optimization during the last decade. It will be a valuable source of information for computer scientists and computational mathematicians.

High-Dimensional Optimization and Probability

Ashkan Nikeghbali,Panos M. Pardalos,Andrei M. Raigorodskii,Michael Th. Rassias
High Dimensional Optimization and Probability Book PDF

Author : Ashkan Nikeghbali,Panos M. Pardalos,Andrei M. Raigorodskii,Michael Th. Rassias
Publisher : Springer Nature
Page : 417 pages
File Size : 45,7 Mb
Release : 2022-08-04
Category : Mathematics
ISBN : 9783031008320

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High-Dimensional Optimization and Probability by Ashkan Nikeghbali,Panos M. Pardalos,Andrei M. Raigorodskii,Michael Th. Rassias Pdf

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.

Advances in Convex Analysis and Global Optimization

Nicolas Hadjisavvas,Panos M. Pardalos
Advances in Convex Analysis and Global Optimization Book PDF

Author : Nicolas Hadjisavvas,Panos M. Pardalos
Publisher : Springer Science & Business Media
Page : 601 pages
File Size : 51,5 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461302797

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Advances in Convex Analysis and Global Optimization by Nicolas Hadjisavvas,Panos M. Pardalos Pdf

There has been much recent progress in global optimization algo rithms for nonconvex continuous and discrete problems from both a theoretical and a practical perspective. Convex analysis plays a fun damental role in the analysis and development of global optimization algorithms. This is due essentially to the fact that virtually all noncon vex optimization problems can be described using differences of convex functions and differences of convex sets. A conference on Convex Analysis and Global Optimization was held during June 5 -9, 2000 at Pythagorion, Samos, Greece. The conference was honoring the memory of C. Caratheodory (1873-1950) and was en dorsed by the Mathematical Programming Society (MPS) and by the Society for Industrial and Applied Mathematics (SIAM) Activity Group in Optimization. The conference was sponsored by the European Union (through the EPEAEK program), the Department of Mathematics of the Aegean University and the Center for Applied Optimization of the University of Florida, by the General Secretariat of Research and Tech nology of Greece, by the Ministry of Education of Greece, and several local Greek government agencies and companies. This volume contains a selective collection of refereed papers based on invited and contribut ing talks presented at this conference. The two themes of convexity and global optimization pervade this book. The conference provided a forum for researchers working on different aspects of convexity and global opti mization to present their recent discoveries, and to interact with people working on complementary aspects of mathematical programming.

Rigorous Global Search: Continuous Problems

R. Baker Kearfott
Rigorous Global Search Continuous Problems Book PDF

Author : R. Baker Kearfott
Publisher : Springer Science & Business Media
Page : 275 pages
File Size : 43,5 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475724950

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Rigorous Global Search: Continuous Problems by R. Baker Kearfott Pdf

This work grew out of several years of research, graduate seminars and talks on the subject. It was motivated by a desire to make the technology accessible to those who most needed it or could most use it. It is meant to be a self-contained introduction, a reference for the techniques, and a guide to the literature for the underlying theory. It contains pointers to fertile areas for future research. It also serves as introductory documentation for a Fortran 90 software package for nonlinear systems and global optimization. The subject of the monograph is deterministic, automatically verified or r- orous methods. In such methods, directed rounding and computational fix- point theory are combined with exhaustive search (branch and bound) te- niques. Completion of such an algorithm with a list of solutions constitutes a rigorous mathematical proof that all of the solutions within the original search region are within the output list. The monograph is appropriate as an introduction to research and technology in the area, as a desk reference, or as a graduate-level course reference. Kno- edge of calculus, linear algebra, and elementary numerical analysis is assumed.