Introduction To Nonsmooth Optimization

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Introduction to Nonsmooth Optimization

Adil Bagirov,Napsu Karmitsa,Marko M. Mäkelä
Introduction to Nonsmooth Optimization Book PDF

Author : Adil Bagirov,Napsu Karmitsa,Marko M. Mäkelä
Publisher : Springer
Page : 372 pages
File Size : 41,9 Mb
Release : 2014-08-12
Category : Business & Economics
ISBN : 9783319081144

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Introduction to Nonsmooth Optimization by Adil Bagirov,Napsu Karmitsa,Marko M. Mäkelä Pdf

This book is the first easy-to-read text on nonsmooth optimization (NSO, not necessarily differentiable optimization). Solving these kinds of problems plays a critical role in many industrial applications and real-world modeling systems, for example in the context of image denoising, optimal control, neural network training, data mining, economics and computational chemistry and physics. The book covers both the theory and the numerical methods used in NSO and provide an overview of different problems arising in the field. It is organized into three parts: 1. convex and nonconvex analysis and the theory of NSO; 2. test problems and practical applications; 3. a guide to NSO software. The book is ideal for anyone teaching or attending NSO courses. As an accessible introduction to the field, it is also well suited as an independent learning guide for practitioners already familiar with the basics of optimization.

Nonsmooth Optimization: Analysis And Algorithms With Applications To Optimal Control

Marko M Makela,Pekka Neittaanmaki
Nonsmooth Optimization Analysis And Algorithms With Applications To Optimal Control Book PDF

Author : Marko M Makela,Pekka Neittaanmaki
Publisher : World Scientific
Page : 268 pages
File Size : 51,8 Mb
Release : 1992-05-07
Category : Mathematics
ISBN : 9789814522410

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Nonsmooth Optimization: Analysis And Algorithms With Applications To Optimal Control by Marko M Makela,Pekka Neittaanmaki Pdf

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.

An Introduction to Nonlinear Optimization Theory

Marius Durea,Radu Strugariu
An Introduction to Nonlinear Optimization Theory Book PDF

Author : Marius Durea,Radu Strugariu
Publisher : Walter de Gruyter GmbH & Co KG
Page : 328 pages
File Size : 44,7 Mb
Release : 2014-01-01
Category : Mathematics
ISBN : 9783110427356

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An Introduction to Nonlinear Optimization Theory by Marius Durea,Radu Strugariu Pdf

The goal of this book is to present the main ideas and techniques in the field of continuous smooth and nonsmooth optimization. Starting with the case of differentiable data and the classical results on constrained optimization problems, and continuing with the topic of nonsmooth objects involved in optimization theory, the book concentrates on both theoretical and practical aspects of this field. This book prepares those who are engaged in research by giving repeated insights into ideas that are subsequently dealt with and illustrated in detail.

Introduction to Functional Analysis

Christian Clason
Introduction to Functional Analysis Book PDF

Author : Christian Clason
Publisher : Springer Nature
Page : 166 pages
File Size : 43,8 Mb
Release : 2020-11-30
Category : Mathematics
ISBN : 9783030527846

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Introduction to Functional Analysis by Christian Clason Pdf

Functional analysis has become one of the essential foundations of modern applied mathematics in the last decades, from the theory and numerical solution of differential equations, from optimization and probability theory to medical imaging and mathematical image processing. This textbook offers a compact introduction to the theory and is designed to be used during one semester, fitting exactly 26 lectures of 90 minutes each. It ranges from the topological fundamentals recalled from basic lectures on real analysis to spectral theory in Hilbert spaces. Special attention is given to the central results on dual spaces and weak convergence.

Nonsmooth Analysis

Winfried Schirotzek
Nonsmooth Analysis Book PDF

Author : Winfried Schirotzek
Publisher : Springer Science & Business Media
Page : 380 pages
File Size : 42,7 Mb
Release : 2007-05-26
Category : Mathematics
ISBN : 9783540713333

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Nonsmooth Analysis by Winfried Schirotzek Pdf

This book treats various concepts of generalized derivatives and subdifferentials in normed spaces, their geometric counterparts and their application to optimization problems. It starts with the subdifferential of convex analysis, passes to corresponding concepts for locally Lipschitz continuous functions and then presents subdifferentials for general lower semicontinuous functions. All basic tools are presented where they are needed: this concerns separation theorems, variational and extremal principles as well as relevant parts of multifunction theory. Each chapter ends with bibliographic notes and exercises.

Nonsmooth Mechanics and Convex Optimization

Yoshihiro Kanno
Nonsmooth Mechanics and Convex Optimization Book PDF

Author : Yoshihiro Kanno
Publisher : CRC Press
Page : 439 pages
File Size : 43,8 Mb
Release : 2011-04-05
Category : Business & Economics
ISBN : 9781420094244

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Nonsmooth Mechanics and Convex Optimization by Yoshihiro Kanno Pdf

"This book concerns matter that is intrinsically difficult: convex optimization, complementarity and duality, nonsmooth analysis, linear and nonlinear programming, etc. The author has skillfully introduced these and many more concepts, and woven them into a seamless whole by retaining an easy and consistent style throughout. The book is not all the

Methods of Dynamic and Nonsmooth Optimization

Frank H. Clarke
Methods of Dynamic and Nonsmooth Optimization Book PDF

Author : Frank H. Clarke
Publisher : SIAM
Page : 95 pages
File Size : 51,9 Mb
Release : 1989-01-01
Category : Mathematics
ISBN : 1611970148

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Methods of Dynamic and Nonsmooth Optimization by Frank H. Clarke Pdf

Presents the elements of a unified approach to optimization based on "nonsmooth analysis," a term introduced in the 1970's by the author, who is a pioneer in the field. Based on a series of lectures given at a conference at Emory University in 1986, this volume presents its subjects in a self-contained and accessible manner. The topics treated here have been in an active state of development, and this work therefore incorporates more recent results than those presented in 1986. Focuses mainly on deterministic optimal control, the calculus of variations, and mathematical programming. In addition, it features a tutorial in nonsmooth analysis and geometry and demonstrates that the method of value function analysis via proximal normals is a powerful tool in the study of necessary conditions, sufficient conditions, controllability, and sensitivity analysis. The distinction between inductive and deductive methods, the use of Hamiltonians, the verification technique, and penalization are also emphasized.

Nonsmooth Approach to Optimization Problems with Equilibrium Constraints

Jiri Outrata,M. Kocvara,J. Zowe
Nonsmooth Approach to Optimization Problems with Equilibrium Constraints Book PDF

Author : Jiri Outrata,M. Kocvara,J. Zowe
Publisher : Springer Science & Business Media
Page : 281 pages
File Size : 48,5 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781475728255

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Nonsmooth Approach to Optimization Problems with Equilibrium Constraints by Jiri Outrata,M. Kocvara,J. Zowe Pdf

In the early fifties, applied mathematicians, engineers and economists started to pay c10se attention to the optimization problems in which another (lower-Ievel) optimization problem arises as a side constraint. One of the motivating factors was the concept of the Stackelberg solution in game theory, together with its economic applications. Other problems have been encountered in the seventies in natural sciences and engineering. Many of them are of practical importance and have been extensively studied, mainly from the theoretical point of view. Later, applications to mechanics and network design have lead to an extension of the problem formulation: Constraints in form of variation al inequalities and complementarity problems were also admitted. The term "generalized bi level programming problems" was used at first but later, probably in Harker and Pang, 1988, a different terminology was introduced: Mathematical programs with equilibrium constraints, or simply, MPECs. In this book we adhere to MPEC terminology. A large number of papers deals with MPECs but, to our knowledge, there is only one monograph (Luo et al. , 1997). This monograph concentrates on optimality conditions and numerical methods. Our book is oriented similarly, but we focus on those MPECs which can be treated by the implicit programming approach: the equilibrium constraint locally defines a certain implicit function and allows to convert the problem into a mathematical program with a nonsmooth objective.

Mathematics of Optimization: Smooth and Nonsmooth Case

Giorgio Giorgi,A. Guerraggio,J. Thierfelder
Mathematics of Optimization Smooth and Nonsmooth Case Book PDF

Author : Giorgio Giorgi,A. Guerraggio,J. Thierfelder
Publisher : Elsevier
Page : 614 pages
File Size : 49,5 Mb
Release : 2004-03-10
Category : Mathematics
ISBN : 9780080535951

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Mathematics of Optimization: Smooth and Nonsmooth Case by Giorgio Giorgi,A. Guerraggio,J. Thierfelder Pdf

The book is intended for people (graduates, researchers, but also undergraduates with a good mathematical background) involved in the study of (static) optimization problems (in finite-dimensional spaces). It contains a lot of material, from basic tools of convex analysis to optimality conditions for smooth optimization problems, for non smooth optimization problems and for vector optimization problems. The development of the subjects are self-contained and the bibliographical references are usually treated in different books (only a few books on optimization theory deal also with vector problems), so the book can be a starting point for further readings in a more specialized literature. Assuming only a good (even if not advanced) knowledge of mathematical analysis and linear algebra, this book presents various aspects of the mathematical theory in optimization problems. The treatment is performed in finite-dimensional spaces and with no regard to algorithmic questions. After two chapters concerning, respectively, introductory subjects and basic tools and concepts of convex analysis, the book treats extensively mathematical programming problems in the smmoth case, in the nonsmooth case and finally vector optimization problems. · Self-contained · Clear style and results are either proved or stated precisely with adequate references · The authors have several years experience in this field · Several subjects (some of them non usual in books of this kind) in one single book, including nonsmooth optimization and vector optimization problems · Useful long references list at the end of each chapter

Nonsmooth Analysis and Control Theory

Francis H. Clarke,Yuri S. Ledyaev,Ronald J. Stern,Peter R. Wolenski
Nonsmooth Analysis and Control Theory Book PDF

Author : Francis H. Clarke,Yuri S. Ledyaev,Ronald J. Stern,Peter R. Wolenski
Publisher : Springer Science & Business Media
Page : 288 pages
File Size : 47,5 Mb
Release : 2008-01-10
Category : Mathematics
ISBN : 9780387226255

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Nonsmooth Analysis and Control Theory by Francis H. Clarke,Yuri S. Ledyaev,Ronald J. Stern,Peter R. Wolenski Pdf

A clear and succinct presentation of the essentials of this subject, together with some of its applications and a generous helping of interesting exercises. Following an introductory chapter with a taste of what is to come, the next three chapters constitute a course in nonsmooth analysis and identify a coherent and comprehensive approach to the subject, leading to an efficient, natural, and powerful body of theory. The whole is rounded off with a self-contained introduction to the theory of control of ordinary differential equations. The authors have incorporated a number of new results which clarify the relationships between the different schools of thought in the subject, with the aim of making nonsmooth analysis accessible to a wider audience. End-of-chapter problems offer scope for deeper understanding.

Derivative-Free and Blackbox Optimization

Charles Audet,Warren Hare
Derivative Free and Blackbox Optimization Book PDF

Author : Charles Audet,Warren Hare
Publisher : Springer
Page : 302 pages
File Size : 44,6 Mb
Release : 2017-12-02
Category : Mathematics
ISBN : 9783319689135

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Derivative-Free and Blackbox Optimization by Charles Audet,Warren Hare Pdf

This book is designed as a textbook, suitable for self-learning or for teaching an upper-year university course on derivative-free and blackbox optimization. The book is split into 5 parts and is designed to be modular; any individual part depends only on the material in Part I. Part I of the book discusses what is meant by Derivative-Free and Blackbox Optimization, provides background material, and early basics while Part II focuses on heuristic methods (Genetic Algorithms and Nelder-Mead). Part III presents direct search methods (Generalized Pattern Search and Mesh Adaptive Direct Search) and Part IV focuses on model-based methods (Simplex Gradient and Trust Region). Part V discusses dealing with constraints, using surrogates, and bi-objective optimization. End of chapter exercises are included throughout as well as 15 end of chapter projects and over 40 figures. Benchmarking techniques are also presented in the appendix.

Optimal Control Via Nonsmooth Analysis

Philip Daniel Loewen
Optimal Control Via Nonsmooth Analysis Book PDF

Author : Philip Daniel Loewen
Publisher : American Mathematical Soc.
Page : 112 pages
File Size : 53,5 Mb
Release : 1993
Category : Control theory
ISBN : 0821869965

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Optimal Control Via Nonsmooth Analysis by Philip Daniel Loewen Pdf

This book provides a complete and unified treatment of deterministic problems of dynamic optimization, from the classical themes of the calculus of variations to the forefront of modern research in optimal control. At the heart of the presentation is nonsmooth analysis, a theory of local approximation developed over the last twenty years to provide useful first-order information about sets and functions lying beyond the reach of classical analysis. The book includes an intuitive and geometrically transparent approach to nonsmooth analysis, serving not only to introduce the basic ideas, but also to illuminate the calculations and derivations in the applied sections dealing with the calculus of variations and optimal control. Written in a lively, engaging style and stocked with numerous figures and practice problems, this book offers an ideal introduction to this vigorous field of current research. It is suitable as a graduate text for a one-semester course in optimal control or as a manual for self-study. Each chapter closes with a list of references to ease the reader's transition from active learner to contributing researcher.

Nonsmooth Optimization in Honor of the 60th Birthday of Adil M. Bagirov

Napsu Karmitsa,Sona Taheri
Nonsmooth Optimization in Honor of the 60th Birthday of Adil M Bagirov Book PDF

Author : Napsu Karmitsa,Sona Taheri
Publisher : MDPI
Page : 116 pages
File Size : 40,8 Mb
Release : 2020-12-18
Category : Science
ISBN : 9783039438358

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Nonsmooth Optimization in Honor of the 60th Birthday of Adil M. Bagirov by Napsu Karmitsa,Sona Taheri Pdf

The aim of this book was to collect the most recent methods developed for NSO and its practical applications. The book contains seven papers: The first is the foreword by the Guest Editors giving a brief review of NSO and its real-life applications and acknowledging the outstanding contributions of Professor Adil Bagirov to both the theoretical and practical aspects of NSO. The second paper introduces a new and very efficient algorithm for solving uncertain unit-commitment (UC) problems. The third paper proposes a new nonsmooth version of the generalized damped Gauss–Newton method for solving nonlinear complementarity problems. In the fourth paper, the abs-linear representation of piecewise linear functions is extended to yield simultaneously their DC decomposition as well as the pair of generalized gradients. The fifth paper presents the use of biased-randomized algorithms as an effective methodology to cope with NP-hard and nonsmooth optimization problems in many practical applications. In the sixth paper, a problem concerning the scheduling of nuclear waste disposal is modeled as a nonsmooth multiobjective mixed-integer nonlinear optimization problem, and a novel method using the two-slope parameterized achievement scalarizing functions is introduced. Finally, the last paper considers binary classification of a multiple instance learning problem and formulates the learning problem as a nonconvex nonsmooth unconstrained optimization problem with a DC objective function.

Introduction to Optimization and Hadamard Semidifferential Calculus, Second Edition

Michel C. Delfour
Introduction to Optimization and Hadamard Semidifferential Calculus Second Edition Book PDF

Author : Michel C. Delfour
Publisher : SIAM
Page : 445 pages
File Size : 42,6 Mb
Release : 2019-12-19
Category : Mathematics
ISBN : 9781611975963

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Introduction to Optimization and Hadamard Semidifferential Calculus, Second Edition by Michel C. Delfour Pdf

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

Nonsmooth Optimization and Related Topics

F.H. Clarke,Vladimir F. Dem'yanov,F. Giannessi
Nonsmooth Optimization and Related Topics Book PDF

Author : F.H. Clarke,Vladimir F. Dem'yanov,F. Giannessi
Publisher : Springer Science & Business Media
Page : 489 pages
File Size : 46,5 Mb
Release : 2013-11-11
Category : Science
ISBN : 9781475760194

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Nonsmooth Optimization and Related Topics by F.H. Clarke,Vladimir F. Dem'yanov,F. Giannessi Pdf

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.