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OverviewThe subject of (static) optimization, also called mathematical programming, is one of the most important and widespread branches of modern mathematics, serving as a cornerstone of such scientific subjects as economic analysis, operations research, management sciences, engineering, chemistry, physics, statistics, computer science, biology, and social sciences. This book presents a unified, progressive treatment of the basic mathematical tools of mathematical programming theory. The authors expose said tools, along with results concerning the most common mathematical programming problems formulated in a finite-dimensional setting, forming the basis for further study of the basic questions on the various algorithmic methods and the most important particular applications of mathematical programming problems. This book assumes no previous experience in optimization theory, and the treatment of the various topics is largely self-contained. Prerequisites are the basic tools of differential calculus for functions of several variables, the basic notions of topology and of linear algebra, and the basic mathematical notions and theoretical background used in analyzing optimization problems. The book is aimed at both undergraduate and postgraduate students interested in mathematical programming problems but also those professionals who use optimization methods and wish to learn the more theoretical aspects of these questions. Full Product DetailsAuthor: Giorgio Giorgi , Bienvenido Jiménez , Vicente NovoPublisher: Springer International Publishing AG Imprint: Springer International Publishing AG Edition: 1st ed. 2023 Volume: 344 Weight: 0.834kg ISBN: 9783031303234ISBN 10: 3031303237 Pages: 433 Publication Date: 19 July 2023 Audience: Professional and scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: Manufactured on demand  We will order this item for you from a manufactured on demand supplier. Table of ContentsPrefaceChapter 1. Basic Notions and Definitions1.1. Introduction1.2. Basic Notions of Analysis and Linear Algebra1.3. Basic Notions and Properties of Optimization ProblemsChapter 2. Elements of Convex Analysis. Theorems of the Alternative for LInear Systems. Tangent Cones2.1. Elements of Convex Analysis2.2. Theorems of the Alternative for Linear Systems2.3. Tangent ConesChapter 3. Convex Functions and Generalized Convex Functions3.1. Convex Functions3.2. Generalized Convex Functions3.3. Optimality Properties of Convex and Generalized ConvexFunctions. Theorems of the Alternative for Nonlinear SystemsChapter 4. Unconstrained Optimization Problems. Set-Constrained Optimiza-tion Problems. Classical Constrained Optimization Problems4.1. Unconstrained Optimization Problems4.2. Set-Constrained Optimization Problems4.3. Optimization Problems with Equality Constraints (“ClassicalConstrained Optimization Problems”)Chapter 5. Constrained OptimizationProblems with Inequality Constraints5.1. First-Order Conditions5.2. Constraint Qualifications5.3. Second-Order Conditions5.4. Other Formulations of the Problem. Some ExamplesChapter 6. Constrained OptimizationProblems with Mixed Constraints6.1. First-Order Conditions6.2. Constraint Qualifications6.3. Second-Order Conditions6.4. Problems with a Set Constraint. Asymptotic OptimalityConditionsChapter 7. Sensitivity Analysis7.1. General Results7.2. Sensitivity Results for Right-Hand Side PerturbationsChapter 8. Convex Optimization: Saddle Points Characterization and Introduction to Duality8.1. Convex Optimization: Saddle Points Characterization8.2. Introduction to DualityChapter 9. Linear Programming andQuadratic Programming9.1. Linear Programming9.2. Duality for Linear Programming9.3. Quadratic ProgrammingChapter 10. Introduction to NonsmoothOptimization Problems10.1. The Convex Case10.2. The Lipschitz Case10.3. The Axiomatic Approach of K.-H. Elster and J. Thierfelderto Nonsmooth Optimization.Chapter 11. Introduction to Multiobjective Optimization11.1. Optimality Notions11.2. The Weighted Sum Method and Optimality ConditionsReferencesIndexReviewsAuthor InformationProf. Giorgio Giorgi teaches Mathematics at the Faculty of Economics of the University of Pavia. His research interests essentially focus on mathematical economics, generalized convexity, and optimization. Bienvenido Jiménez and Vicente Novo are professors of Applied Mathematics at the National University of Distance Education, Madrid, Spain. Their research focus on smooth and nonsmooth optimization, mathematical programming and multiobjective, vector and set optimization. Tab Content 6Author Website:Countries AvailableAll regions |
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