This book studies the problems of stability and well-posedness, in the convex case. Stability means the basic parameters of a minimum problem do not vary much if we slightly change the initial data, while well-posedness means points with values close to the value of the problem must be close to actual solutions. In studying this, one is naturally led to consider perturbations of functions and of sets.

This book contains a condensed explication of hypertopologies and is intended to help those not familiar with hypertopologies learn how to use them in the context of optimization problems.

Contains a chapter on hypertopologies (only one other book on this topic) Author includes exercises, for use as a graduate text Over 45 figures are included Includes supplementary material: sn.pub/extras

Inhalt
Convex sets and convex functions: the fundamentals.- Continuity and ?(X).- The derivatives and the subdifferential.- Minima and quasi minima.- The Fenchel conjugate.- Duality.- Linear programming and game theory.- Hypertopologies, hyperconvergences.- Continuity of some operations between functions.- Well-posed problems.- Generic well-posedness.- More exercises.