03968nam 2200625Ia 450 991084152210332120170810191550.01-280-36700-897866103670090-470-31182-70-471-46166-00-471-24970-X(CKB)111087027121356(EBL)157071(OCoLC)475872690(SSID)ssj0000130321(PQKBManifestationID)11146398(PQKBTitleCode)TC0000130321(PQKBWorkID)10082121(PQKB)11452153(MiAaPQ)EBC157071(PPN)169570053(EXLCZ)9911108702712135620010706d2002 uy 0engur|n|---|||||txtccrConvexity and optimization in R [superscript n][electronic resource] /Leonard D. BerkovitzNew York J. Wileyc20021 online resource (283 p.)Pure and applied mathematicssDescription based upon print version of record.0-471-35281-0 Includes bibliographical references (p. 261-262) and index.CONVEXITY AND OPTIMIZATION IN R(n); CONTENTS; Preface; I Topics in Real Analysis; 1. Introduction; 2. Vectors in R(n); 3. Algebra of Sets; 4. Metric Topology of R(n); 5. Limits and Continuity; 6. Basic Property of Real Numbers; 7. Compactness; 8. Equivalent Norms and Cartesian Products; 9. Fundamental Existence Theorem; 10. Linear Transformations; 11. Differentiation in R(n); II Convex Sets in R(n); 1. Lines and Hyperplanes in R(n); 2. Properties of Convex Sets; 3. Separation Theorems; 4. Supporting Hyperplanes: Extreme Points; 5. Systems of Linear Inequalities: Theorems of the Alternative6. Affine Geometry7. More on Separation and Support; III Convex Functions; 1. Definition and Elementary Properties; 2. Subgradients; 3. Differentiable Convex Functions; 4. Alternative Theorems for Convex Functions; 5. Application to Game Theory; IV Optimization Problems; 1. Introduction; 2. Differentiable Unconstrained Problems; 3. Optimization of Convex Functions; 4. Linear Programming Problems; 5. First-Order Conditions for Differentiable Nonlinear Programming Problems; 6. Second-Order Conditions; V Convex Programming and Duality; 1. Problem Statement2. Necessary Conditions and Sufficient Conditions3. Perturbation Theory; 4. Lagrangian Duality; 5. Geometric Interpretation; 6. Quadratic Programming; 7. Duality in Linear Programming; VI Simplex Method; 1. Introduction; 2. Extreme Points of Feasible Set; 3. Preliminaries to Simplex Method; 4. Phase II of Simplex Method; 5. Termination and Cycling; 6. Phase I of Simplex Method; 7. Revised Simplex Method; Bibliography; IndexA comprehensive introduction to convexity and optimization in RnThis book presents the mathematics of finite dimensional constrained optimization problems. It provides a basis for the further mathematical study of convexity, of more general optimization problems, and of numerical algorithms for the solution of finite dimensional optimization problems. For readers who do not have the requisite background in real analysis, the author provides a chapter covering this material. The text features abundant exercises and problems designed to lead the reader to a fundamental understanding of tPure and applied mathematics (John Wiley & Sons : Unnumbered)Convex setsMathematical optimizationConvex sets.Mathematical optimization.516/.08519.3Berkovitz Leonard David1924-283994MiAaPQMiAaPQMiAaPQBOOK9910841522103321Convexity and optimization in R4139435UNINA