Tangential extremal principles for finite and infinite systems of sets, I: basic theory

• Published in: Mathematical programming Vol. 136; no. 1; pp. 3 - 30
• Main Authors: Mordukhovich, Boris S., Phan, Hung M.
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 01.12.2012; Springer; Springer Nature B.V
• Subjects: Applied sciences; Approximation; Calculus of variations and optimal control; Calculus of Variations and Optimal Control; Optimization; Combinatorics; Decision theory. Utility theory; Exact sciences and technology; Flows in networks. Combinatorial problems; Full Length Paper; Mathematical analysis; Mathematical and Computational Physics; Mathematical Methods in Physics; Mathematical programming; Mathematics; Mathematics and Statistics; Mathematics of Computing; Names; Numerical Analysis; Operational research and scientific management; Operational research. Management science; Optimization; Principles; Programming; Sciences and techniques of general use; Shadow prices; Studies; Theoretical; Variational analysis; Semi-infinite programming; 49J53; Multiobjective optimization; Extremal systems; Extremal principles; Tangent and normal cones; Secondary 90C30; Primary 49J52; Cone; Convex set; Multiobjective programming; Semi infinite programming; Semi-infinite programing; Infinite system; Approximation algorithm; Combinatorial optimization; Extremum problem; Primal dual method; Variational principle; Variational calculus; Set theory; Non convex analysis; Mathematical programming
• ISSN: 0025-5610; 1436-4646
• DOI: 10.1007/s10107-012-0549-4

In this paper we develop new extremal principles in variational analysis that deal with finite and infinite systems of convex and nonconvex sets. The results obtained, unified under the name of tangential extremal principles, combine primal and dual approaches to the study of variational systems being in fact first extremal principles applied to infinite systems of sets. The first part of the paper concerns the basic theory of tangential extremal principles while the second part presents applications to problems of semi-infinite programming and multiobjective optimization.