Fréchet vector subdifferential calculus

On subdifferential calculus ∗

The main purpose of these lectures is to familiarize the student with the basic ingredients of convex analysis, especially its subdifferential calculus. This is done while moving to a clearly discernible end-goal, the Karush-Kuhn-Tucker theorem, which is one of the main results of nonlinear programming. Of course, in the present lectures we have to limit ourselves most of the time to the Karush...

Elements of Quasiconvex Subdifferential Calculus

A number of rules for the calculus of subdifferentials of generalized convex functions are displayed. The subdifferentials we use are among the most significant for this class of functions, in particular for quasiconvex functions: we treat the Greenberg-Pierskalla’s subdifferential and its relatives and the Plastria’s lower subdifferential. We also deal with a recently introduced subdifferentia...

Metric Inequality, Subdifferential Calculus and Applications

In this paper, we establish characterizations of Asplund spaces in terms of conditions ensuring the metric inequality and intersection formulae. Then we establish chain rules for the limiting Fréchet subdifferentials. Necessary conditions for constrained optimization problems with non-Lipschitz data are derived.

Fréchet on the Calculus of Probability

Towards Supremum-Sum Subdifferential Calculus Free of Qualification Conditions