Stationarity and Regularity Concepts for Set Systems
The paper investigates stationarity and regularity concepts for set systems in a normed space. Several primal and dual constants characterizing these properties are introduced and the relations between the constants are established. The equivalence between the regularity property and the strong metric inequality is established. The extended extremal principle is formulated.
keywordsnonsmooth analysis normal cone optimality extremality stationarity regularity set-valued mapping Asplund space
- D. Klatte, B. Kummer. Nonsmooth Equations in Optimization: Regularity, Calculus, Methods and Applications. Kluwer Academic Publishers, Dordrecht, 2002.Google Scholar
- A.Y. Kruger. About regularity of set systems. Research Report, University of Ballarat, School of Information Technology and Mathematical Sciences, N. 3, 2005.Google Scholar
- B.S. Mordukhovich. The extremal principle and its applications to optimization and economics. In Optimization and Related Topics, A. Rubinov and B. Glover, eds., Applied Optimization, Vol. 47, Kluwer Academic Publishers, Dordrecht, 2001, 343–369.Google Scholar