| This book is an abridged version of our two-volume opus Convex Analysis and Minimization Algorithms [18], about which we have received very positive feedback from users, readers, lecturers ever since it was published-by Springer-Verlag in 1993. Its pedagogical qualities were particularly appreciated, in the combination with a rather advanced technical material. |
| Preface O. Introduction: Notation， Elementary Results 1 Some Facts About Lower and Upper Bounds 2 The Set of Extended Real Numbers 3 Linear and Bilinear Algebra 4 Differentiation in a Euclidean Space 5 Set-Valued Analysis 6 Recalls on Convex Functions of the Real Variable Exercises A. Convex Sets 1 Generalities 2 Convex Sets Attached to a Convex Set 3 Projection onto Closed Convex Sets 4 Separation and Applications 5 Conical Approximations of Convex Sets Exercises B. Convex Functions 1 Basic Definitions and Examples 2 Functional Operations Preserving Convexity 3 Local and Global Behaviour of a Convex Function 4 First-and Second-Order Differentiation Preface O. Introduction: Notation， Elementary Results 1 Some Facts About Lower and Upper Bounds 2 The Set of Extended Real Numbers 3 Linear and Bilinear Algebra 4 Differentiation in a Euclidean Space 5 Set-Valued Analysis 6 Recalls on Convex Functions of the Real Variable Exercises A. Convex Sets 1 Generalities 2 Convex Sets Attached to a Convex Set 3 Projection onto Closed Convex Sets 4 Separation and Applications 5 Conical Approximations of Convex Sets Exercises C. Sublinearity and Support Functions 1 Sublinear Functions 2 The Support Function of a Nonempty Set 3 Correspondence Between Convex Sets and Sublinear Functions Exercises D. Subdifferentials of Finite Convex Functions 1 The Subdifferential:Definitions and Interpretations 2 Local Properties of the Subdiffrential 3 First Examples 4 Calculus Rules with Subdifferentials 5 Further Examples 6 The Subdifferential as a Multifunction Exercises E. Conjugacy in Convex Analysis 1 The Convex Conjugate of a Function 2 Calculus Rules on the Conjugacy Operation 3 Various Examples 4 Differentiability of a Conjugate Function Exercises Bibliographical Comments The Founding Fathers of the Discipline References Index |
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