This little book has evolved from my experience in teaching convex analysis
at the University of Utrecht, Holland. In theory and applications, convex
analysis is of increasing interest at the present time. This book is primarily
an introductory text; therefore I have tried to emphasize the basic concepts
and the characteristic methods of this part of mathematics (such as separation,
subgradient, conjugate function, convex optimization). A large number
of elementary exercises at the ends of the various chapters (with answers
and hints at the end of the book) are intended to aid in understanding the
concepts employed.
The book is intended for the young student who is interested in convexity
and whose mathematical background includes the basic facts of calculus,
linear algebra, and general topology; it is also supposed that he is acquainted
with the basic concepts of functional analysis (such as normed
linear space, Hilbert space, dual).
In order to convey the flavour of the subject and to arouse the student's
interest, I have not restricted myself to the finite-dimensional case one
usually deals with in practice. But to keep things as simple as possible, of the
class of locally convex spaces, the 'natural' domain of convex analysis, only
normed spaces appear in this book. 荷兰学者撰写的一本杰出的凸分析引论教材，凸分析在数理经济学中有着广泛的应用。