Convexity and Well-Posed Problems

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.