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010   $a9786610367009
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010   $a0-471-46166-0
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100   $a20010706d2002      uy         0
101 0 $aeng
135   $aur|n|---|||||
181   $ctxt
182   $cc
183   $acr
200 10$aConvexity and optimization in R [superscript n]$b[electronic resource] /$fLeonard D. Berkovitz
210   $aNew York $cJ. Wiley$dc2002
215   $a1 online resource (283 p.)
225 1 $aPure and applied mathematicss
300   $aDescription based upon print version of record.
311   $a0-471-35281-0 
320   $aIncludes bibliographical references (p. 261-262) and index.
327   $aCONVEXITY 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 Alternative
327   $a6. 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 Statement
327   $a2. 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; Index
330   $aA comprehensive introduction to convexity and optimization in RnThis book presents the mathematics of finite dimensional constrained optimization problems. It provides a basis for the further mathematical study of convexity, of more general optimization problems, and of numerical algorithms for the solution of finite dimensional optimization problems. For readers who do not have the requisite background in real analysis, the author provides a chapter covering this material. The text features abundant exercises and problems designed to lead the reader to a fundamental understanding of t
410  0$aPure and applied mathematics (John Wiley & Sons : Unnumbered)
606   $aConvex sets
606   $aMathematical optimization
615  0$aConvex sets.
615  0$aMathematical optimization.
676   $a516/.08
676   $a519.3
700   $aBerkovitz$b Leonard David$f1924-$0283994
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910841522103321
996   $aConvexity and optimization in R$94139435
997   $aUNINA