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### **RESCHEDULED**: Notes on the Ekeland variational principle

**Optimization**

Speaker: | Gerald Beer, California State University at Los Angeles |

Location: | 2112 MSB |

Start time: | Fri, Jun 3 2011, 12:00PM |

We introduce standard forms of the Ekeland variational principle, a fundamental tool in optimization theory and its applications. We show that the weak Ekeland variational principle is itself derivative of a geometric principle for lower bounded Lipschitz real-valued functions. Both the weak Ekeland principle and our principle for Lipschitz functions are characteristic of completeness of the underlying metric. We use this new principle to directly obtain an omnibus result regarding the nonempty intersection of a decreasing sequence of nonempty closed sets. We also characterize a class of metric spaces lying strictly between the compact and complete metric spaces by an Ekeland-type principle: the class of metric spaces $X$ on which each continuous functions with values in an arbitrary metric space is uniformly continuous.