Fundamentals of convex analysis
Jean-Baptiste Hiriart-Urruty, Claude Lemaréchal
Introduction: Notation, Elementary Results.- Convex Sets: Generalities; Convex Sets Attached to a Convex Set; Projection onto Closed Convex Sets; Separation and Applications; Conical Approximations of Convex Sets.- Convex Functions: Basic Definitions and Examples; Functional Operations Preserving Convexity; Local and Global Behaviour of a Convex Function; First- and Second-Order Differentiation.- Sublinearity and Support Functions: Sublinear Functions; The Support Function of a Nonempty Set; Correspondence Between Convex Sets and Sublinear Functions.- Subdifferentials of Finite Convex Functions: The Subdifferential: Definitions and Interpretations; Local Properties of the Subdifferential; First Examples; Calculus Rules with Subdifferentials; Further Examples; The Subdifferential as a Multifunction.- Conjugacy in Convex Analysis: The Convex Conjugate of a Function; Calculus Rules on the Conjugacy Operation; Various Examples; Differentiability of a Conjugate Function
หมวดหมู่:
ปี:
2001
สำนักพิมพ์:
Springer
ภาษา:
english
จำนวนหน้า:
269
ISBN 10:
3540422056
ISBN 13:
9783540422051
ซีรีส์:
Grundlehren text editions
ไฟล์:
DJVU, 2.34 MB
IPFS:
,
english, 2001