文档介绍：Mathematics of Optimization
Smooth and Nonsmooth Case
by G. i, Angelo Guerraggio, J. Thierfelder
· ISBN: 0444505504
· Publisher: Elsevier Science & Technology Books
· Pub. Date: March 2004
PREFACE
The present book is primarily dedicated to the study of the optimal-
ity conditions for a nonlinear programming problem, also known as a
mathematical programming problem. Indeed one of the main subjects of
mathematical optimization (a relatively modern branch of applied math•
ematics which has grown at an exponential rate, both from a theoretical
point of view and on the side of applications) is the study of a class of ex-
tremum problems where the objective function / is to be optimized under
some restrictions, usually in the form of equalities and/or inequalities.
As an example for a nonlinear programming problem in R^, we mean
an extremum problem of the following type:
Min f{x) (F)
xes
where S = {x e X \ gi{x) ^ 0, z = l,...,m; hk{x) = 0, /c = l,...,p},
XcR'\ f,guhk:X^R.
If all the functions involved in (P) are linear, we speak of linear pro•
gramming problems. A more general version of (P) is one where the
objective function / is a vector-valued function. This latter case (espe•
cially important from an economic point of view) will be treated in the
last chapter of the book.
Problems similar to (P) arise in several contexts: the building and inter•
preting of economic models; the study of various technological processes;
the development of optimal choices in finance; operations research; man•
agement science; production processes; transportation models; statistical
decisions, etc. Therefore it is of the utmost importance to study the exis•
tence of solutions for (P) and to study the effective methods (. numerical
algorithms) for finding solutions of the problem. This second aspect of the
study of (P) will not be treated here; we shall be concerned only with
the study of the optimality condi