Title Convex analysis and nonlinear optimization : theory and examples / Jonathan M. Borwein, Adrian S. Lewis

Edition Second edition Published New York : Springer, [2006] ©2006

Copies

Location	Call no.	Vol.	Availability
MELB	515.8 Bor/Caa 2006		AVAILABLE

Description xii, 310 pages ; 25 cm Series CMS books in mathematics ; 3 CMS books in mathematics ; 3 Contents Machine derived contents note: 1 Background 1 -- 1.1 Euclidean Spaces 1 -- 1.2 Symmetric Matrices 9 -- 2 Inequality Constraints 15 -- 2.1 Optimality Conditions 15 -- 2.2 Theorems of the Alternative 23 -- 2.3 Max-functions 28 -- 3 Fenchel Duality 33 -- 3.1 Subgradients and Convex Functions 33 -- 3.2 The Value Function 43 -- 3.3 The Fenchel Conjugate 49 -- 4 Convex Analysis 65 -- 4.1 Continuity of Convex Functions 65 -- 4.2 Fenchel Biconjugation 76 -- 4.3 Lagrangian Duality 88 -- 5 Special Cases 97 -- 5.1 Polyhedral Convex Sets and Functions 97 -- 5.2 Functions of Eigenvalues 104 -- 5.3 Duality for Linear and Semidefinite Programming 109 -- 5.4 Convex Process Duality 114 -- 6 Nonsmooth Optimization 123 -- 6.1 Generalized Derivatives 123 -- 6.2 Regularity and Strict Differentiability 130 -- 6.3 Tangent Cones 137 -- 6.4 The Limiting Subdifferential 145 -- 7 Karush-Kuhn-Tucker Theory 153 -- 7.1 An Introduction to Metric Regularity 153 -- 7.2 The Karush-Kuhn-Tucker Theorem 160 -- 7.3 Metric Regularity and the Limiting Subdifferential 166 -- 7.4 Second Order Conditions 172 -- 8 Fixed Points 179 -- 8.1 The Brouwer Fixed Point Theorem 179 -- 8.2 Selection and the Kakutani-Fan Fixed Point Theorem 190 -- 8.3 Variational Inequalities 200 -- 9 More Nonsmooth Structure 213 -- 9.1 Rademacher's Theorem 213 -- 9.2 Proximal Normals and Chebyshev Sets 218 -- 9.3 Amenable Sets and Prox-Regularity 228 -- 9.4 Partly Smooth Sets 233 -- 10 Postscript: Infinite Versus Finite Dimensions 239 -- 10.1 Introduction 239 -- 10.2 Finite Dimensionality 241 -- 10.3 Counterexamples and Exercises 244 -- 10.4 Notes on Previous Chapters 248 -- 11 List of Results and Notation 253 -- 11.1 Named Results. 253 -- 11.2 Notation 267 Bibliography Includes bibliographical references (pages 275-288) and index Subject Convex functions. Mathematical optimization. Nonlinear theories. Author Lewis, Adrian S. LC no. 2005934031 ISBN 0387295704 9780387295701

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