On Minimizing and Critical Sequences in Nonsmooth Optimization

Let f be a bounded below, lower semicontinuous function from a Banach space into $R\cup \{+\infty \}.$ We study the relationships between minimizing and critical sequences of f, where the criticality condition is given in terms of some subdifferential $\partial.$ Here the objective function f is not supposed to be convex or smooth. Our work extends that of Auslender and Crouzeix and that of Chou, Ng, and Pang.