Methods of Dynamic and Nonsmooth Optimization
Methods of Dynamic and Nonsmooth Optimization

Author: Frank H. Clarke

Publisher: SIAM

Published: 1989-01-01

Total Pages: 94

ISBN-13: 0898712416

DOWNLOAD EBOOK

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. 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.

Methods of Dynamic and Nonsmooth Optimization
Methods of Dynamic and Nonsmooth Optimization

Author: Frank H. Clarke

Publisher: SIAM

Published: 1989-01-01

Total Pages: 95

ISBN-13: 9781611970142

DOWNLOAD EBOOK

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 Optimization
Nonsmooth Optimization

Author: Claude Lemarechal

Publisher: Elsevier

Published: 2014-05-19

Total Pages: 195

ISBN-13: 1483188760

DOWNLOAD EBOOK

Nonsmooth Optimization contains the proceedings of a workshop on non-smooth optimization (NSO) held from March 28 to April 8,1977 in Austria under the auspices of the International Institute for Applied Systems Analysis. The papers explore the techniques and theory of NSO and cover topics ranging from systems of inequalities to smooth approximation of non-smooth functions, as well as quadratic programming and line searches. Comprised of nine chapters, this volume begins with a survey of Soviet research on subgradient optimization carried out since 1962, followed by a discussion on rates of convergence in subgradient optimization. The reader is then introduced to the method of subgradient optimization in an abstract setting and the minimal hypotheses required to ensure convergence; NSO and nonlinear programming; and bundle methods in NSO. A feasible descent algorithm for linearly constrained least squares problems is described. The book also considers sufficient minimization of piecewise-linear univariate functions before concluding with a description of the method of parametric decomposition in mathematical programming. This monograph will be of interest to mathematicians and mathematics students.

Encyclopedia of Optimization
Encyclopedia of Optimization

Author: Christodoulos A. Floudas

Publisher: Springer Science & Business Media

Published: 2008-09-04

Total Pages: 4646

ISBN-13: 0387747583

DOWNLOAD EBOOK

The goal of the Encyclopedia of Optimization is to introduce the reader to a complete set of topics that show the spectrum of research, the richness of ideas, and the breadth of applications that has come from this field. The second edition builds on the success of the former edition with more than 150 completely new entries, designed to ensure that the reference addresses recent areas where optimization theories and techniques have advanced. Particularly heavy attention resulted in health science and transportation, with entries such as "Algorithms for Genomics", "Optimization and Radiotherapy Treatment Design", and "Crew Scheduling".

Nonlinear Programming
Nonlinear Programming

Author: Lorenz T. Biegler

Publisher: SIAM

Published: 2010-01-01

Total Pages: 411

ISBN-13: 0898719380

DOWNLOAD EBOOK

This book addresses modern nonlinear programming (NLP) concepts and algorithms, especially as they apply to challenging applications in chemical process engineering. The author provides a firm grounding in fundamental NLP properties and algorithms, and relates them to real-world problem classes in process optimization, thus making the material understandable and useful to chemical engineers and experts in mathematical optimization.

Modern Nonconvex Nondifferentiable Optimization
Modern Nonconvex Nondifferentiable Optimization

Author: Ying Cui

Publisher: Society for Industrial and Applied Mathematics (SIAM)

Published: 2022

Total Pages: 0

ISBN-13: 9781611976731

DOWNLOAD EBOOK

"This monograph serves present and future needs where nonconvexity and nondifferentiability are inevitably present in the faithful modeling of real-world applications of optimization"--

Numerical Nonsmooth Optimization
Numerical Nonsmooth Optimization

Author: Adil M. Bagirov

Publisher: Springer Nature

Published: 2020-02-28

Total Pages: 696

ISBN-13: 3030349101

DOWNLOAD EBOOK

Solving nonsmooth optimization (NSO) problems is critical in many practical applications and real-world modeling systems. The aim of this book is to survey various numerical methods for solving NSO problems and to provide an overview of the latest developments in the field. Experts from around the world share their perspectives on specific aspects of numerical NSO. The book is divided into four parts, the first of which considers general methods including subgradient, bundle and gradient sampling methods. In turn, the second focuses on methods that exploit the problem’s special structure, e.g. algorithms for nonsmooth DC programming, VU decomposition techniques, and algorithms for minimax and piecewise differentiable problems. The third part considers methods for special problems like multiobjective and mixed integer NSO, and problems involving inexact data, while the last part highlights the latest advancements in derivative-free NSO. Given its scope, the book is ideal for students attending courses on numerical nonsmooth optimization, for lecturers who teach optimization courses, and for practitioners who apply nonsmooth optimization methods in engineering, artificial intelligence, machine learning, and business. Furthermore, it can serve as a reference text for experts dealing with nonsmooth optimization.

Recent Advances in Fuzzy Sets Theory, Fractional Calculus, Dynamic Systems and Optimization
Recent Advances in Fuzzy Sets Theory, Fractional Calculus, Dynamic Systems and Optimization

Author: Said Melliani

Publisher: Springer Nature

Published: 2022-08-10

Total Pages: 496

ISBN-13: 3031124162

DOWNLOAD EBOOK

We describe in this book recent advances in fuzzy sets theory, fractional calculus, dynamic systems, and optimization. The book provides a setting for the discussion of recent developments in a wide variety of topics including partial differential equations, dynamic systems, optimization, numerical analysis, fuzzy sets theory, fractional calculus, and its applications. The book is aimed at bringing together contributions from leading academic scientists, researchers, and research scholars to exchange and share their experiences and research results on all aspects of applied mathematics, modeling, algebra, economics, finance, and applications. It also provides an interdisciplinary platform for researchers, practitioners, and educators to present the most recent innovations, trends, and concerns as well as practical challenges encountered and solutions adopted in the fields of applied mathematics. The published chapters address various aspects of academic scientists, researchers, and research scholars in many variety mathematical topics.

Dynamic Treatment Regimes
Dynamic Treatment Regimes

Author: Anastasios A. Tsiatis

Publisher: CRC Press

Published: 2019-12-19

Total Pages: 602

ISBN-13: 1498769780

DOWNLOAD EBOOK

Dynamic Treatment Regimes: Statistical Methods for Precision Medicine provides a comprehensive introduction to statistical methodology for the evaluation and discovery of dynamic treatment regimes from data. Researchers and graduate students in statistics, data science, and related quantitative disciplines with a background in probability and statistical inference and popular statistical modeling techniques will be prepared for further study of this rapidly evolving field. A dynamic treatment regime is a set of sequential decision rules, each corresponding to a key decision point in a disease or disorder process, where each rule takes as input patient information and returns the treatment option he or she should receive. Thus, a treatment regime formalizes how a clinician synthesizes patient information and selects treatments in practice. Treatment regimes are of obvious relevance to precision medicine, which involves tailoring treatment selection to patient characteristics in an evidence-based way. Of critical importance to precision medicine is estimation of an optimal treatment regime, one that, if used to select treatments for the patient population, would lead to the most beneficial outcome on average. Key methods for estimation of an optimal treatment regime from data are motivated and described in detail. A dedicated companion website presents full accounts of application of the methods using a comprehensive R package developed by the authors. The authors’ website www.dtr-book.com includes updates, corrections, new papers, and links to useful websites.