Convex Functions, Monotone Operators And Differentiability (lecture Notes In Mathematics)
by Robert R. Phelps /
1993 / English / PDF
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The improved and expanded second edition contains expositions of
some major results which have been obtained in the years since the
1st edition. Theaffirmative answer by Preiss of the decades old
question of whether a Banachspace with an equivalent Gateaux
differentiable norm is a weak Asplund space. The startlingly simple
proof by Simons of Rockafellar's fundamental maximal monotonicity
theorem for subdifferentials of convex functions. The exciting new
version of the useful Borwein-Preiss smooth variational principle
due to Godefroy, Deville and Zizler. The material is accessible to
students who have had a course in Functional Analysis; indeed, the
first edition has been used in numerous graduate seminars. Starting
with convex functions on the line, it leads to interconnected
topics in convexity, differentiability and subdifferentiability of
convex functions in Banach spaces, generic continuity of monotone
operators, geometry of Banach spaces and the Radon-Nikodym
property, convex analysis, variational principles and perturbed
optimization. While much of this is classical, streamlined proofs
found more recently are given in many instances. There are numerous
exercises, many of which form an integral part of the exposition.
The improved and expanded second edition contains expositions of
some major results which have been obtained in the years since the
1st edition. Theaffirmative answer by Preiss of the decades old
question of whether a Banachspace with an equivalent Gateaux
differentiable norm is a weak Asplund space. The startlingly simple
proof by Simons of Rockafellar's fundamental maximal monotonicity
theorem for subdifferentials of convex functions. The exciting new
version of the useful Borwein-Preiss smooth variational principle
due to Godefroy, Deville and Zizler. The material is accessible to
students who have had a course in Functional Analysis; indeed, the
first edition has been used in numerous graduate seminars. Starting
with convex functions on the line, it leads to interconnected
topics in convexity, differentiability and subdifferentiability of
convex functions in Banach spaces, generic continuity of monotone
operators, geometry of Banach spaces and the Radon-Nikodym
property, convex analysis, variational principles and perturbed
optimization. While much of this is classical, streamlined proofs
found more recently are given in many instances. There are numerous
exercises, many of which form an integral part of the exposition.