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In this paper we develop new extremal principles in variational analysis thatdeal with finite and infinite systems of convex and nonconvex sets. The resultsobtained, unified under the name of tangential extremal principles, combineprimal and dual approaches to the study of variational systems being in factfirst extremal principles applied to infinite systems of sets. The first partof the paper concerns the basic theory of tangential extremal principles whilethe second part presents applications to problems of semi-infinite programmingand multiobjective optimization.

Tangential Extremal Principles for Finite and Infinite Systems of Sets, I: Basic Theory