The German edition of this book, first published in 1966, has been quite
popular; we did not, however, consider publishing an English edition
because a number of excellent textbooks in this field already exist. In
recent years, how- ever, the wish was frequently expressed that,
especially, the description of the relationships between optimization
and other subfields of mathematics, which is not to be found in this
form in other texts, might be made available to a wider readership; so
it was with this in mind that, be- latedly, a translation was undertaken
after all. Since the appearance of the German edition, the field of
optimization has continued to develop at an unabated rate. A completely
current presentation would have required a total reworking of the book;
unfortunately, this was not possible. For example, we had to ignore the
extensive progress which has been made in the development of numerical
methods which do not require convexity assumptions to find local maxima
and minima of non-linear optimization problems. These methods are also
applicable to boundary value, and other, problems. Many new results,
both of a numerical and a theoretical na- ture, which are especially
relevant to applications, are to be found in the areas of optimal contol
and integer optimiza- tion.