TABLE OF CONTENTS This appendix provides some background material on those aspects of real analysis and optimization which are frequently used in the text; it also serves to introduce the reader to our notation and terminology. For a more detailed exposition on the topics covered here, a standard reference is Luenberger (1969).
A set S is a collection of elements. If s is a member (element) of S, we write s ? S; if s does not belong to S, we write 
. If S contains a finite number of elements, it is called a finite set; otherwise it is called an infinite set. If the number of elements of an infinite set is countable (i.e., if there is a one-to-one correspondence between its elements and positive integers), we say that it is a denumerable (countable) set, otherwise it is a nondenumerable set.
A set S with some specific structure attached to it is called a space, and it is called a linear (vector) space if this specific structure is of algebraic nature with certain well-known properties which we assume that the reader is familiar with. If S is a vector space, a subset of S which is also a vector space is called a subspace. An example of a vector space is the n-dimensional Euclidean space (denoted by R n) each element of which is determined by n real numbers. An
