LEADER 05959nam 22006495 450 001 9910735090803321 005 20251113205032.0 010 $a3-031-30324-5 024 7 $a10.1007/978-3-031-30324-1 035 $a(CKB)27671053300041 035 $a(DE-He213)978-3-031-30324-1 035 $a(MiAaPQ)EBC30766871 035 $a(Au-PeEL)EBL30766871 035 $a(PPN)272250252 035 $a(MiAaPQ)EBC30651753 035 $a(Au-PeEL)EBL30651753 035 $a(EXLCZ)9927671053300041 100 $a20230718d2023 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aBasic Mathematical Programming Theory /$fby Giorgio Giorgi, Bienvenido Jiménez, Vicente Novo 205 $a1st ed. 2023. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2023. 215 $a1 online resource (XII, 433 p. 19 illus., 7 illus. in color.) 225 1 $aInternational Series in Operations Research & Management Science,$x2214-7934 ;$v344 311 08$a9783031303234 320 $aIncludes bibliographical references and index. 327 $aPreface -- Chapter 1. Basic Notions and Definitions -- 1.1. Introduction -- 1.2. Basic Notions of Analysis and Linear Algebra -- 1.3. Basic Notions and Properties of Optimization Problems -- Chapter 2. Elements of Convex Analysis. Theorems of the Alternative for Linear Systems. Tangent Cones -- 2.1. Elements of Convex Analysis -- 2.2. Theorems of the Alternative for Linear Systems -- 2.3. Tangent Cones -- Chapter 3. Convex Functions and Generalized Convex Functions -- 3.1. Convex Functions -- 3.2. Generalized Convex Functions -- 3.3. Optimality Properties of Convex and Generalized Convex Functions. Theorems of the Alternative for Nonlinear Systems -- Chapter 4. Unconstrained Optimization Problems. Set-Constrained Optimization Problems. Classical Constrained Optimization Problems -- 4.1. Unconstrained Optimization Problems -- 4.2. Set-Constrained Optimization Problems -- 4.3. Optimization Problems with Equality Constraints (?Classical Constrained Optimization Problems?) -- Chapter 5. Constrained Optimization Problems with Inequality Constraints -- 5.1. First-Order Conditions -- 5.2. Constraint Qualifications -- 5.3. Second-Order Conditions -- 5.4. Other Formulations of the Problem. Some Examples -- Chapter 6. Constrained Optimization Problems with Mixed Constraints -- 6.1. First-Order Conditions -- 6.2. Constraint Qualifications -- 6.3. Second-Order Conditions -- 6.4. Problems with a Set Constraint. Asymptotic Optimality Conditions -- Chapter 7.Sensitivity Analysis -- 7.1. General Results -- 7.2. Sensitivity Results for Right-Hand Side Perturbations -- Chapter 8. Convex Optimization: Saddle Points Characterization and Introduction to Duality -- 8.1. Convex Optimization: Saddle Points Characterization -- 8.2. Introduction to Duality -- Chapter 9. Linear Programming and Quadratic Programming -- 9.1. Linear Programming -- 9.2. Duality for Linear Programming -- 9.3. Quadratic Programming -- Chapter 10. Introduction to Nonsmooth Optimization Problems -- 10.1. The Convex Case -- 10.2. The Lipschitz Case -- 10.3.The Axiomatic Approach of K.-H. Elster and J. Thierfelder to Nonsmooth Optimization -- Chapter 11. Introduction to Multiobjective Optimization -- 11.1. Optimality Notions -- 11.2. The Weighted Sum Method and Optimality Conditions -- References -- Index. 330 $aThis book presents a unified, progressive treatment of the basic mathematical tools of mathematical programming theory. The subject of (static) optimization, also called mathematical programming, is one of the most important and widespread branches of modern mathematics, serving as a cornerstone of such scientific subjects as economic analysis, operations research, management sciences, engineering, chemistry, physics, statistics, computer science, biology, and social sciences. This book presents a unified, progressive treatment of the basic mathematical tools of mathematical programming theory. The authors expose said tools, along with results concerning the most common mathematical programming problems formulated in a finite-dimensional setting, forming the basis for further study of the basic questions on the various algorithmic methods and the most important particular applications of mathematical programming problems. This book assumes no previous experience in optimization theory, and the treatment of the various topics is largely self-contained. Prerequisites are the basic tools of differential calculus for functions of several variables, the basic notions of topology in Rn and of linear algebra, and the basic mathematical notions and theoretical background used in analyzing optimization problems. The book is aimed at both undergraduate and postgraduate students interested in mathematical programming problems but also those professionals who use optimization methods and wish to learn the more theoretical aspects of these questions. 410 0$aInternational Series in Operations Research & Management Science,$x2214-7934 ;$v344 606 $aOperations research 606 $aMathematical optimization 606 $aAlgebras, Linear 606 $aOperations Research and Decision Theory 606 $aOptimization 606 $aLinear Algebra 615 0$aOperations research. 615 0$aMathematical optimization. 615 0$aAlgebras, Linear. 615 14$aOperations Research and Decision Theory. 615 24$aOptimization. 615 24$aLinear Algebra. 676 $a519.7 676 $a519.7 700 $aGiorgi$b Giorgio$0227678 702 $aJime?nez$b Bienvenido 702 $aNovo$b Vicente 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910735090803321 996 $aBasic Mathematical Programming Theory$93563489 997 $aUNINA