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Author : Arrigo Cellina
Publisher : Springer
ISBN 13 : 3540467157
Total Pages : 214 pages
Book Rating : 4.5/5 (44 download)
Download or read book Methods of Nonconvex Analysis written by Arrigo Cellina and published by Springer. This book was released on 2006-11-14 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Prateek Jain
Publisher : Foundations and Trends in Machine Learning
ISBN 13 : 9781680833683
Total Pages : 218 pages
Book Rating : 4.8/5 (336 download)
Download or read book Non-convex Optimization for Machine Learning written by Prateek Jain and published by Foundations and Trends in Machine Learning. This book was released on 2017-12-04 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: Non-convex Optimization for Machine Learning takes an in-depth look at the basics of non-convex optimization with applications to machine learning. It introduces the rich literature in this area, as well as equips the reader with the tools and techniques needed to apply and analyze simple but powerful procedures for non-convex problems. Non-convex Optimization for Machine Learning is as self-contained as possible while not losing focus of the main topic of non-convex optimization techniques. The monograph initiates the discussion with entire chapters devoted to presenting a tutorial-like treatment of basic concepts in convex analysis and optimization, as well as their non-convex counterparts. The monograph concludes with a look at four interesting applications in the areas of machine learning and signal processing, and exploring how the non-convex optimization techniques introduced earlier can be used to solve these problems. The monograph also contains, for each of the topics discussed, exercises and figures designed to engage the reader, as well as extensive bibliographic notes pointing towards classical works and recent advances. Non-convex Optimization for Machine Learning can be used for a semester-length course on the basics of non-convex optimization with applications to machine learning. On the other hand, it is also possible to cherry pick individual portions, such the chapter on sparse recovery, or the EM algorithm, for inclusion in a broader course. Several courses such as those in machine learning, optimization, and signal processing may benefit from the inclusion of such topics.
Author : Dumitru Motreanu
Publisher : Springer Science & Business Media
ISBN 13 : 9781402013850
Total Pages : 400 pages
Book Rating : 4.0/5 (138 download)
Download or read book Variational and Non-variational Methods in Nonlinear Analysis and Boundary Value Problems written by Dumitru Motreanu and published by Springer Science & Business Media. This book was released on 2003-05-31 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book reflects a significant part of authors' research activity dur ing the last ten years. The present monograph is constructed on the results obtained by the authors through their direct cooperation or due to the authors separately or in cooperation with other mathematicians. All these results fit in a unitary scheme giving the structure of this work. The book is mainly addressed to researchers and scholars in Pure and Applied Mathematics, Mechanics, Physics and Engineering. We are greatly indebted to Viorica Venera Motreanu for the careful reading of the manuscript and helpful comments on important issues. We are also grateful to our Editors of Kluwer Academic Publishers for their professional assistance. Our deepest thanks go to our numerous scientific collaborators and friends, whose work was so important for us. D. Motreanu and V. Radulescu IX Introduction The present monograph is based on original results obtained by the authors in the last decade. This book provides a comprehensive expo sition of some modern topics in nonlinear analysis with applications to the study of several classes of boundary value problems. Our framework includes multivalued elliptic problems with discontinuities, variational inequalities, hemivariational inequalities and evolution problems. The treatment relies on variational methods, monotonicity principles, topo logical arguments and optimization techniques. Excepting Sections 1 and 3 in Chapter 1 and Sections 1 and 3 in Chapter 2, the material is new in comparison with any other book, representing research topics where the authors contributed. The outline of our work is the following.
Author : Ying Cui
Publisher : Society for Industrial and Applied Mathematics (SIAM)
ISBN 13 : 9781611976731
Total Pages : 0 pages
Book Rating : 4.9/5 (767 download)
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"--
Author : David Yang Gao
Publisher : Springer Science & Business Media
ISBN 13 : 9780792361459
Total Pages : 476 pages
Book Rating : 4.3/5 (614 download)
Download or read book Duality Principles in Nonconvex Systems written by David Yang Gao and published by Springer Science & Business Media. This book was released on 2000-01-31 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: Motivated by practical problems in engineering and physics, drawing on a wide range of applied mathematical disciplines, this book is the first to provide, within a unified framework, a self-contained comprehensive mathematical theory of duality for general non-convex, non-smooth systems, with emphasis on methods and applications in engineering mechanics. Topics covered include the classical (minimax) mono-duality of convex static equilibria, the beautiful bi-duality in dynamical systems, the interesting tri-duality in non-convex problems and the complicated multi-duality in general canonical systems. A potentially powerful sequential canonical dual transformation method for solving fully nonlinear problems is developed heuristically and illustrated by use of many interesting examples as well as extensive applications in a wide variety of nonlinear systems, including differential equations, variational problems and inequalities, constrained global optimization, multi-well phase transitions, non-smooth post-bifurcation, large deformation mechanics, structural limit analysis, differential geometry and non-convex dynamical systems. With exceptionally coherent and lucid exposition, the work fills a big gap between the mathematical and engineering sciences. It shows how to use formal language and duality methods to model natural phenomena, to construct intrinsic frameworks in different fields and to provide ideas, concepts and powerful methods for solving non-convex, non-smooth problems arising naturally in engineering and science. Much of the book contains material that is new, both in its manner of presentation and in its research development. A self-contained appendix provides some necessary background from elementary functional analysis. Audience: The book will be a valuable resource for students and researchers in applied mathematics, physics, mechanics and engineering. The whole volume or selected chapters can also be recommended as a text for both senior undergraduate and graduate courses in applied mathematics, mechanics, general engineering science and other areas in which the notions of optimization and variational methods are employed.
Author : Radoslaw Pytlak
Publisher : Springer Science & Business Media
ISBN 13 : 354085634X
Total Pages : 493 pages
Book Rating : 4.5/5 (48 download)
Download or read book Conjugate Gradient Algorithms in Nonconvex Optimization written by Radoslaw Pytlak and published by Springer Science & Business Media. This book was released on 2008-11-18 with total page 493 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Diethard Klatte
Publisher : Springer Science & Business Media
ISBN 13 : 0306476169
Total Pages : 351 pages
Book Rating : 4.3/5 (64 download)
Download or read book Nonsmooth Equations in Optimization written by Diethard Klatte and published by Springer Science & Business Media. This book was released on 2005-12-17 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many questions dealing with solvability, stability and solution methods for va- ational inequalities or equilibrium, optimization and complementarity problems lead to the analysis of certain (perturbed) equations. This often requires a - formulation of the initial model being under consideration. Due to the specific of the original problem, the resulting equation is usually either not differ- tiable (even if the data of the original model are smooth), or it does not satisfy the assumptions of the classical implicit function theorem. This phenomenon is the main reason why a considerable analytical inst- ment dealing with generalized equations (i.e., with finding zeros of multivalued mappings) and nonsmooth equations (i.e., the defining functions are not c- tinuously differentiable) has been developed during the last 20 years, and that under very different viewpoints and assumptions. In this theory, the classical hypotheses of convex analysis, in particular, monotonicity and convexity, have been weakened or dropped, and the scope of possible applications seems to be quite large. Briefly, this discipline is often called nonsmooth analysis, sometimes also variational analysis. Our book fits into this discipline, however, our main intention is to develop the analytical theory in close connection with the needs of applications in optimization and related subjects. Main Topics of the Book 1. Extended analysis of Lipschitz functions and their generalized derivatives, including ”Newton maps” and regularity of multivalued mappings. 2. Principle of successive approximation under metric regularity and its - plication to implicit functions.
Author : Tim Roughgarden
Publisher : Cambridge University Press
ISBN 13 : 1108494315
Total Pages : 705 pages
Book Rating : 4.1/5 (84 download)
Download or read book Beyond the Worst-Case Analysis of Algorithms written by Tim Roughgarden and published by Cambridge University Press. This book was released on 2021-01-14 with total page 705 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduces exciting new methods for assessing algorithms for problems ranging from clustering to linear programming to neural networks.
Author : Marko M Makela
Publisher : World Scientific
ISBN 13 : 9814522414
Total Pages : 268 pages
Book Rating : 4.8/5 (145 download)
Download or read book Nonsmooth Optimization: Analysis And Algorithms With Applications To Optimal Control written by Marko M Makela and published by World Scientific. This book was released on 1992-05-07 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a self-contained elementary study for nonsmooth analysis and optimization, and their use in solution of nonsmooth optimal control problems. The first part of the book is concerned with nonsmooth differential calculus containing necessary tools for nonsmooth optimization. The second part is devoted to the methods of nonsmooth optimization and their development. A proximal bundle method for nonsmooth nonconvex optimization subject to nonsmooth constraints is constructed. In the last part nonsmooth optimization is applied to problems arising from optimal control of systems covered by partial differential equations. Several practical problems, like process control and optimal shape design problems are considered.
Author : David Yang Gao
Publisher : Springer Science & Business Media
ISBN 13 : 9780792367864
Total Pages : 528 pages
Book Rating : 4.3/5 (678 download)
Download or read book Nonsmooth/Nonconvex Mechanics written by David Yang Gao and published by Springer Science & Business Media. This book was released on 2001-03-31 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonsmooth and nonconvex models arise in several important applications of mechanics and engineering. The interest in this field is growing from both mathematicians and engineers. The study of numerous industrial applications, including contact phenomena in statics and dynamics or delamination effects in composites, require the consideration of nonsmoothness and nonconvexity. The mathematical topics discussed in this book include variational and hemivariational inequalities, duality, complementarity, variational principles, sensitivity analysis, eigenvalue and resonance problems, and minimax problems. Applications are considered in the following areas among others: nonsmooth statics and dynamics, stability of quasi- static evolution processes, friction problems, adhesive contact and debonding, inverse problems, pseudoelastic modeling of phase transitions, chaotic behavior in nonlinear beams, and nonholonomic mechanical systems. This volume contains 22 chapters written by various leading researchers and presents a cohesive and authoritative overview of recent results and applications in the area of nonsmooth and nonconvex mechanics. Audience: Faculty, graduate students, and researchers in applied mathematics, optimization, control and engineering.
Author : Stephen P. Boyd
Publisher : Cambridge University Press
ISBN 13 : 9780521833783
Total Pages : 744 pages
Book Rating : 4.8/5 (337 download)
Download or read book Convex Optimization written by Stephen P. Boyd and published by Cambridge University Press. This book was released on 2004-03-08 with total page 744 pages. Available in PDF, EPUB and Kindle. Book excerpt: Convex optimization problems arise frequently in many different fields. This book provides a comprehensive introduction to the subject, and shows in detail how such problems can be solved numerically with great efficiency. The book begins with the basic elements of convex sets and functions, and then describes various classes of convex optimization problems. Duality and approximation techniques are then covered, as are statistical estimation techniques. Various geometrical problems are then presented, and there is detailed discussion of unconstrained and constrained minimization problems, and interior-point methods. The focus of the book is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. It contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance and economics.
Author : Dumitru Motreanu
Publisher : Springer Science & Business Media
ISBN 13 : 1475769210
Total Pages : 384 pages
Book Rating : 4.4/5 (757 download)
Download or read book Variational and Non-variational Methods in Nonlinear Analysis and Boundary Value Problems written by Dumitru Motreanu and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book reflects a significant part of authors' research activity dur ing the last ten years. The present monograph is constructed on the results obtained by the authors through their direct cooperation or due to the authors separately or in cooperation with other mathematicians. All these results fit in a unitary scheme giving the structure of this work. The book is mainly addressed to researchers and scholars in Pure and Applied Mathematics, Mechanics, Physics and Engineering. We are greatly indebted to Viorica Venera Motreanu for the careful reading of the manuscript and helpful comments on important issues. We are also grateful to our Editors of Kluwer Academic Publishers for their professional assistance. Our deepest thanks go to our numerous scientific collaborators and friends, whose work was so important for us. D. Motreanu and V. Radulescu IX Introduction The present monograph is based on original results obtained by the authors in the last decade. This book provides a comprehensive expo sition of some modern topics in nonlinear analysis with applications to the study of several classes of boundary value problems. Our framework includes multivalued elliptic problems with discontinuities, variational inequalities, hemivariational inequalities and evolution problems. The treatment relies on variational methods, monotonicity principles, topo logical arguments and optimization techniques. Excepting Sections 1 and 3 in Chapter 1 and Sections 1 and 3 in Chapter 2, the material is new in comparison with any other book, representing research topics where the authors contributed. The outline of our work is the following.
Author : Ivar Ekeland
Publisher : SIAM
ISBN 13 : 9781611971088
Total Pages : 414 pages
Book Rating : 4.9/5 (71 download)
Download or read book Convex Analysis and Variational Problems written by Ivar Ekeland and published by SIAM. This book was released on 1999-12-01 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains different developments of infinite dimensional convex programming in the context of convex analysis, including duality, minmax and Lagrangians, and convexification of nonconvex optimization problems in the calculus of variations (infinite dimension). It also includes the theory of convex duality applied to partial differential equations; no other reference presents this in a systematic way. The minmax theorems contained in this book have many useful applications, in particular the robust control of partial differential equations in finite time horizon. First published in English in 1976, this SIAM Classics in Applied Mathematics edition contains the original text along with a new preface and some additional references.
Author : Dimitri Bertsekas
Publisher : Athena Scientific
ISBN 13 : 1886529280
Total Pages : 576 pages
Book Rating : 4.8/5 (865 download)
Download or read book Convex Optimization Algorithms written by Dimitri Bertsekas and published by Athena Scientific. This book was released on 2015-02-01 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive and accessible presentation of algorithms for solving convex optimization problems. It relies on rigorous mathematical analysis, but also aims at an intuitive exposition that makes use of visualization where possible. This is facilitated by the extensive use of analytical and algorithmic concepts of duality, which by nature lend themselves to geometrical interpretation. The book places particular emphasis on modern developments, and their widespread applications in fields such as large-scale resource allocation problems, signal processing, and machine learning. The book is aimed at students, researchers, and practitioners, roughly at the first year graduate level. It is similar in style to the author's 2009"Convex Optimization Theory" book, but can be read independently. The latter book focuses on convexity theory and optimization duality, while the present book focuses on algorithmic issues. The two books share notation, and together cover the entire finite-dimensional convex optimization methodology. To facilitate readability, the statements of definitions and results of the "theory book" are reproduced without proofs in Appendix B.
Author : William W. Hager
Publisher : Springer Science & Business Media
ISBN 13 : 038729550X
Total Pages : 416 pages
Book Rating : 4.3/5 (872 download)
Download or read book Multiscale Optimization Methods and Applications written by William W. Hager and published by Springer Science & Business Media. This book was released on 2006-06-18 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: As optimization researchers tackle larger and larger problems, scale interactions play an increasingly important role. One general strategy for dealing with a large or difficult problem is to partition it into smaller ones, which are hopefully much easier to solve, and then work backwards towards the solution of original problem, using a solution from a previous level as a starting guess at the next level. This volume contains 22 chapters highlighting some recent research. The topics of the chapters selected for this volume are focused on the development of new solution methodologies, including general multilevel solution techniques, for tackling difficult, large-scale optimization problems that arise in science and industry. Applications presented in the book include but are not limited to the circuit placement problem in VLSI design, a wireless sensor location problem, optimal dosages in the treatment of cancer by radiation therapy, and facility location.
Author : Stanislav Uryasev
Publisher : Springer Science & Business Media
ISBN 13 : 1475731507
Total Pages : 319 pages
Book Rating : 4.4/5 (757 download)
Download or read book Probabilistic Constrained Optimization written by Stanislav Uryasev and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probabilistic and percentile/quantile functions play an important role in several applications, such as finance (Value-at-Risk), nuclear safety, and the environment. Recently, significant advances have been made in sensitivity analysis and optimization of probabilistic functions, which is the basis for construction of new efficient approaches. This book presents the state of the art in the theory of optimization of probabilistic functions and several engineering and finance applications, including material flow systems, production planning, Value-at-Risk, asset and liability management, and optimal trading strategies for financial derivatives (options). Audience: The book is a valuable source of information for faculty, students, researchers, and practitioners in financial engineering, operation research, optimization, computer science, and related areas.
Author : Dimitri Bertsekas
Publisher : Athena Scientific
ISBN 13 : 1886529450
Total Pages : 560 pages
Book Rating : 4.8/5 (865 download)
Download or read book Convex Analysis and Optimization written by Dimitri Bertsekas and published by Athena Scientific. This book was released on 2003-03-01 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: A uniquely pedagogical, insightful, and rigorous treatment of the analytical/geometrical foundations of optimization. The book provides a comprehensive development of convexity theory, and its rich applications in optimization, including duality, minimax/saddle point theory, Lagrange multipliers, and Lagrangian relaxation/nondifferentiable optimization. It is an excellent supplement to several of our books: Convex Optimization Theory (Athena Scientific, 2009), Convex Optimization Algorithms (Athena Scientific, 2015), Nonlinear Programming (Athena Scientific, 2016), Network Optimization (Athena Scientific, 1998), and Introduction to Linear Optimization (Athena Scientific, 1997). Aside from a thorough account of convex analysis and optimization, the book aims to restructure the theory of the subject, by introducing several novel unifying lines of analysis, including: 1) A unified development of minimax theory and constrained optimization duality as special cases of duality between two simple geometrical problems. 2) A unified development of conditions for existence of solutions of convex optimization problems, conditions for the minimax equality to hold, and conditions for the absence of a duality gap in constrained optimization. 3) A unification of the major constraint qualifications allowing the use of Lagrange multipliers for nonconvex constrained optimization, using the notion of constraint pseudonormality and an enhanced form of the Fritz John necessary optimality conditions. Among its features the book: a) Develops rigorously and comprehensively the theory of convex sets and functions, in the classical tradition of Fenchel and Rockafellar b) Provides a geometric, highly visual treatment of convex and nonconvex optimization problems, including existence of solutions, optimality conditions, Lagrange multipliers, and duality c) Includes an insightful and comprehensive presentation of minimax theory and zero sum games, and its connection with duality d) Describes dual optimization, the associated computational methods, including the novel incremental subgradient methods, and applications in linear, quadratic, and integer programming e) Contains many examples, illustrations, and exercises with complete solutions (about 200 pages) posted at the publisher's web site http://www.athenasc.com/convexity.html
