› › Introduction To Nonsmooth Optimization

Nonsmooth Optimization: Analysis And Algorithms With Applications To Optimal Control

Author : Marko M Makela

Publisher : World Scientific

Page : 268 pages

File Size : 21,96 MB

Release : 1992-05-07

Category : Mathematics

ISBN : 9814522414

Get eBook

Book Description

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.



Introduction to Nonsmooth Optimization

Author : Adil Bagirov

Publisher : Springer

Page : 377 pages

File Size : 35,83 MB

Release : 2014-08-12

Category : Business & Economics

ISBN : 3319081144

Get eBook

Book Description

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.



An Introduction to Nonlinear Optimization Theory

Author : Marius Durea

Publisher : Walter de Gruyter GmbH & Co KG

Page : 398 pages

File Size : 37,67 MB

Release : 2014-01-01

Category : Mathematics

ISBN : 3110427354

Get eBook

Book Description

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

Author : Christian Clason

Publisher : Springer Nature

Page : 166 pages

File Size : 46,49 MB

Release : 2020-11-30

Category : Mathematics

ISBN : 3030527840

Get eBook

Book Description

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 Approach to Optimization Problems with Equilibrium Constraints

Author : Jiri Outrata

Publisher : Springer Science & Business Media

Page : 281 pages

File Size : 24,24 MB

Release : 2013-06-29

Category : Mathematics

ISBN : 1475728255

Get eBook

Book Description

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.



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

Author : Napsu Karmitsa

Publisher : MDPI

Page : 116 pages

File Size : 39,13 MB

Release : 2020-12-18

Category : Science

ISBN : 3039438352

Get eBook

Book Description

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.



Nonsmooth Analysis

Author : Winfried Schirotzek

Publisher : Springer Science & Business Media

Page : 380 pages

File Size : 49,84 MB

Release : 2007-05-26

Category : Mathematics

ISBN : 3540713336

Get eBook

Book Description

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.



Introduction to Optimization and Hadamard Semidifferential Calculus, Second Edition

Author : Michel C. Delfour

Publisher : SIAM

Page : 446 pages

File Size : 25,15 MB

Release : 2019-12-19

Category : Mathematics

ISBN : 1611975964

Get eBook

Book Description

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 Analysis and Control Theory

Author : Francis H. Clarke

Publisher : Springer Science & Business Media

Page : 288 pages

File Size : 16,65 MB

Release : 2008-01-10

Category : Mathematics

ISBN : 0387226257

Get eBook

Book Description

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.



Nonsmooth Mechanics and Convex Optimization

Author : Yoshihiro Kanno

Publisher : CRC Press

Page : 439 pages

File Size : 46,87 MB

Release : 2011-04-05

Category : Business & Economics

ISBN : 1420094246

Get eBook

Book Description

"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



Recent Books