H.M.: Rated extremal principles for finite and infinite systems

Abstract. In this paper we introduce new notions of local extremality for finite and infinite systems of closed sets and establish the corresponding extremal principles for them called here rated extremal principles. These developments are in the core geometric theory of variational analysis. We present their applications to calculus and optimality conditions for problems with infinitely many constraints. Key words. Variational analysis, extremal principles, generalized normals, calculus rules, infinite intersections, semi-infinite and infinite optimization, necessary optimality condition