Variational analysis and generalized differentiation, I, basic theory / Boris S. Mordukhovich

...The principal objective in these two volumes is to present basic concepts and principles of variational analysis unified in finite-dimensional and infinite-dimensional settings, to develop a comprehensive generalized differential theory at the same level of perfection in both finite and infinite dimensions, and to provide valuable applications of variational theory to broad classes of problems in constrained optimization and equilibrium, sensitivity and stability analysis, control theory for ordinary, functional-differential and partial differential equations, and also to selected problems in mechanics and economics. The author develops generalized differentiation by using a geometric dual-space approach, which revolves around the extremal principle, namely, a local variational counterpart of the classical convex separation in nonconvex settings. ... (Zentralblatt)