This book aims to present, in a unified way, some basic aspects of the mathematical
theory of well-posedness in scalar optimization.
The first fundamental concept in this area is inspired by the classical idea of J.
Hadamard, which goes back to the beginning of this century. It requires existence and
uniqueness of the optimal solution together with continuous dependence on the problem's
data.
In the early sixties A. Tykhonov introduced another concept of well-posedness
imposing convergence of every minimizing sequence to the unique minimum point. Its relevance
to (and motivation from) the approximate (numerical) solution of optimization problems
is clear.
In the book we study both the Tykhonov and the Hadamard concepts of well-posedness,
the links between them and also some extensions (e.g. relaxing the uniqueness).
Both the pure and the applied sides of our topic are presented. The first four chapters
are devoted to abstract optimization problems. Applications to optimal control, c&'cuius
of variations and mathematical programming are the subject matter of the remaining five
chapters.