Rated extremal principles for finite and infinite systems

Abstract

In this article we introduce new notions of local extremality for finite and infinite systems of closed sets and establish the corresponding extremal principles for them, here called 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.

Keywords:

• variational analysis
• extremal principles
• generalized normals
• calculus rules
• infinite intersections
• semi-infinite and infinite optimization
• necessary optimality conditions

AMS Subject Classifications::

• Primary: 49J52, 49J53
• Secondary: 90C30

Acknowledgements

This research was partially supported by the US National Science Foundation under grants DMS-0603846 and DMS-1007132 and by the Australian Research Council under grant DP-12092508.