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Mathematics of optimizationsmooth an...

Giorgi, G.

Mathematics of optimizationsmooth and nonsmooth case /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Mathematics of optimizationG. Giorgi, A. Guerraggio, J. Thierfelder.
Reminder of title:	smooth and nonsmooth case /
Author:	Giorgi, G.
other author:	Thierfelder, J.
Published:	Amsterdam ;Elsevier,2004.
Description:	xv, 598 p. ;24 cm.
Subject:	Mathematical optimization.
Online resource:	An electronic book accessible through the World Wide Web; click for information
Online resource:	http://www.loc.gov/catdir/toc/els051/2004040362.html
Online resource:	http://www.loc.gov/catdir/description/els051/2004040362.html
ISBN:	9780444505507

Mathematics of optimizationsmooth and nonsmooth case /
Giorgi, G.

Mathematics of optimizationsmooth and nonsmooth case /[electronic resource] :G. Giorgi, A. Guerraggio, J. Thierfelder. - 1st ed. - Amsterdam ;Elsevier,2004. - xv, 598 p. ;24 cm.

Includes bibliographical references and index.

Contents -- Preface. -- CHAPTER I.INTRODUCTION. -- 1.1 Optimization Problems. -- 1.2 Basic Mathematical Preliminaries and Notations. -- References to Chapter I. -- CHAPTER II.CONVEX SETS, CONVEX AND GENERALIZED CONVEX FUNCTIONS. -- 2.1 Convex Sets and Their Main Properties. -- 2.2 Separation Theorems. -- 2.3 Some Particular Convex Sets. Convex Cone. -- 2.4 Theorems of the Alternative for Linear Systems. -- 2.5 Convex Functions. -- 2.6 Directional Derivatives and Subgradients of Convex Functions. -- 2.7 Conjugate Functions. -- 2.8 Extrema of Convex Functions. -- 2.9 Systems of Convex Functions and Nonlinear Theorems of the Alternative. -- 2.10 Generalized Convex Functions. -- 2.11 Relationships Between the Various Classes of Generalized Convex Functions. Properties in Optimization Problems. -- 2.12 Generalized Monotonicity and Generalized Convexity. -- 2.13 Comparison Between Convex and Generalized Convex Functions. -- 2.14 Generalized Convexity at a Point. -- 2.15 Convexity, Pseudoconvexity and Quasiconvexity of Composite Functions. -- 2.16 Convexity, Pseudoconvexity and Quasiconvexity of Quadratic Functions. -- 2.17 Other Types of Generalized Convex Functions References to Chapter II. -- CHAPTER III.SMOOTH OPTIMIZATION PROBLEMS -- SADDLE POINT CONDITIONS. -- 3.1 Introduction. -- 3.2 Unconstrained Extremum Problems and Extremum -- Problems with a Set Constraint. -- 3.3 Equality Constrained Extremum Problems. -- 3.4 Local Cone Approximations of Sets. -- 3.5 Necessary Optimality Conditions for Problem (P) where the Optimal Point is Interior to X. -- 3.6 Necessary Optimality Conditions for Problems (P e); and The Case of a Set Constraint. -- 3.7 Again on Constraint Qualifications. -- 3.8 Necessary Optimality Conditions for (P 1). -- 3.9 Sufficient First-Order Optimality Conditions for (P) and (P 1). -- 3.10 Second-Order Optimality Conditions. -- 3.11 Linearization Properties of a Nonlinear Programming Problem. -- 3.12 Some Specific Cases. -- 3.13 Extensions to Topological Spaces. -- 3.14 Optimality Criteria of the Saddle Point Type References to Chapter III -- CHAPTER IV. NONSMOOTH OPTIMIZATION PROBLEMS. -- 4.1 Preliminary Remarks. -- 4.2 Differentiability. -- 4.3 Directional Derivatives and Subdifferentials for Convex Functions. -- 4.4 Generalized Directional Derivatives. -- 4.5 Generalized Gradient Mappings. -- 4.6 Abstract Cone Approximations of Sets and Relating Differentiability Notions. -- 4.7 Special K-Directional Derivative. -- 4.8 Generalized Optimality Conditions. -- References to Chapter IV -- CHAPTER V. DUALITY. -- 5.1 Preliminary Remarks. -- 5.2 Duality in Linear Optimization. -- 5.3 Duality in Convex Optimization (Wolfe Duality). -- 5.4 Lagrange Duality. -- 5.5 Perturbed Optimization Problems. -- References to Chapter V -- CHAPTER VI. VECTOR OPTIMIZATION. -- 6.1 Vector Optimization Problems. -- 6.2 Conical Preference Orders. -- 6.3 Optimality (or Efficiency) Notions. -- 6.4 Proper Efficiency. -- 6.5 Theorems of Existence. -- 6.6 Optimality Conditions. -- 6.7 Scalarization. -- 6.8 The Nondifferentiable Case. -- References to Chapter VI. -- SUBJECT INDEX.

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.

Electronic reproduction.
Amsterdam :
Elsevier Science & Technology,
2007.

Mode of access: World Wide Web.

ISBN: 9780444505507

Source: 107948:107990Elsevier Science & Technologyhttp://www.sciencedirect.comSubjects--Topical Terms:

183292
Mathematical optimization.
Index Terms--Genre/Form:

214472
Electronic books.

LC Class. No.: QA402.5 / .G55 2004eb

Dewey Class. No.: 519.6

Mathematics of optimizationsmooth and nonsmooth case /
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245 1 0 $a Mathematics of optimization $h [electronic resource] : $b smooth and nonsmooth case / $c G. Giorgi, A. Guerraggio, J. Thierfelder.
250 $a 1st ed.
260 $a Amsterdam ; $a Boston : $c 2004. $b Elsevier,
300 $a xv, 598 p. ; $c 24 cm.
504 $a Includes bibliographical references and index.
505 0 $a Contents -- Preface. -- CHAPTER I.INTRODUCTION. -- 1.1 Optimization Problems. -- 1.2 Basic Mathematical Preliminaries and Notations. -- References to Chapter I. -- CHAPTER II.CONVEX SETS, CONVEX AND GENERALIZED CONVEX FUNCTIONS. -- 2.1 Convex Sets and Their Main Properties. -- 2.2 Separation Theorems. -- 2.3 Some Particular Convex Sets. Convex Cone. -- 2.4 Theorems of the Alternative for Linear Systems. -- 2.5 Convex Functions. -- 2.6 Directional Derivatives and Subgradients of Convex Functions. -- 2.7 Conjugate Functions. -- 2.8 Extrema of Convex Functions. -- 2.9 Systems of Convex Functions and Nonlinear Theorems of the Alternative. -- 2.10 Generalized Convex Functions. -- 2.11 Relationships Between the Various Classes of Generalized Convex Functions. Properties in Optimization Problems. -- 2.12 Generalized Monotonicity and Generalized Convexity. -- 2.13 Comparison Between Convex and Generalized Convex Functions. -- 2.14 Generalized Convexity at a Point. -- 2.15 Convexity, Pseudoconvexity and Quasiconvexity of Composite Functions. -- 2.16 Convexity, Pseudoconvexity and Quasiconvexity of Quadratic Functions. -- 2.17 Other Types of Generalized Convex Functions References to Chapter II. -- CHAPTER III.SMOOTH OPTIMIZATION PROBLEMS -- SADDLE POINT CONDITIONS. -- 3.1 Introduction. -- 3.2 Unconstrained Extremum Problems and Extremum -- Problems with a Set Constraint. -- 3.3 Equality Constrained Extremum Problems. -- 3.4 Local Cone Approximations of Sets. -- 3.5 Necessary Optimality Conditions for Problem (P) where the Optimal Point is Interior to X. -- 3.6 Necessary Optimality Conditions for Problems (P e); and The Case of a Set Constraint. -- 3.7 Again on Constraint Qualifications. -- 3.8 Necessary Optimality Conditions for (P 1). -- 3.9 Sufficient First-Order Optimality Conditions for (P) and (P 1). -- 3.10 Second-Order Optimality Conditions. -- 3.11 Linearization Properties of a Nonlinear Programming Problem. -- 3.12 Some Specific Cases. -- 3.13 Extensions to Topological Spaces. -- 3.14 Optimality Criteria of the Saddle Point Type References to Chapter III -- CHAPTER IV. NONSMOOTH OPTIMIZATION PROBLEMS. -- 4.1 Preliminary Remarks. -- 4.2 Differentiability. -- 4.3 Directional Derivatives and Subdifferentials for Convex Functions. -- 4.4 Generalized Directional Derivatives. -- 4.5 Generalized Gradient Mappings. -- 4.6 Abstract Cone Approximations of Sets and Relating Differentiability Notions. -- 4.7 Special K-Directional Derivative. -- 4.8 Generalized Optimality Conditions. -- References to Chapter IV -- CHAPTER V. DUALITY. -- 5.1 Preliminary Remarks. -- 5.2 Duality in Linear Optimization. -- 5.3 Duality in Convex Optimization (Wolfe Duality). -- 5.4 Lagrange Duality. -- 5.5 Perturbed Optimization Problems. -- References to Chapter V -- CHAPTER VI. VECTOR OPTIMIZATION. -- 6.1 Vector Optimization Problems. -- 6.2 Conical Preference Orders. -- 6.3 Optimality (or Efficiency) Notions. -- 6.4 Proper Efficiency. -- 6.5 Theorems of Existence. -- 6.6 Optimality Conditions. -- 6.7 Scalarization. -- 6.8 The Nondifferentiable Case. -- References to Chapter VI. -- SUBJECT INDEX.
520 $a 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.
533 $a Electronic reproduction. $b Amsterdam : $c Elsevier Science & Technology, $d 2007. $n Mode of access: World Wide Web. $n System requirements: Web browser. $n Title from title screen (viewed on July 25, 2007). $n Access may be restricted to users at subscribing institutions.
650 0 $a Mathematical optimization. $3 183292
650 0 $a Nonlinear programming. $3 185871
650 7 $a Programa�c�ao matem�atica. $2 larpcal $3 340808
650 7 $a Otimiza�c�ao matem�atica. $2 larpcal $3 340809
655 7 $a Electronic books. $2 local. $3 214472
700 1 $a Thierfelder, J. $q (J�org) $3 452593
700 1 $a Guerraggio, Angelo, $d 1948- $3 340805
710 2 $a ScienceDirect (Online service) $3 307425
856 4 0 $3 ScienceDirect $u http://www.sciencedirect.com/science/book/9780444505507 $z An electronic book accessible through the World Wide Web; click for information
856 4 1 $3 Table of contents $u http://www.loc.gov/catdir/toc/els051/2004040362.html
856 4 2 $3 Publisher description $u http://www.loc.gov/catdir/description/els051/2004040362.html
994 $a C0 $b TEF

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