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Abstracts of Lectures
Alexander Ioffe: Variational Analysis in Metric Spaces
Adrian Lewis: Eigenvalue Optimization and Non-Smooth Analysis
"Nonsmooth analysis", an ambitious and elegant extension
of classical calculus and optimization, has blossomed over
recent decades. But is it useful? In particular, can it
help us understand and solve concrete, finite-dimensional
optimization problems? Cogent supporting evidence comes
from "eigenvalue optimization", the study of variational
problems involving the eigenvalues of symmetric and
nonsymmetric matrices. Such problems ("semidefinite
programming" is an example) arise often, particularly in
engineering design. Since eigenvalues are nonsmooth
functions of the underlying matrix, the theory and
computational practice of eigenvalue optimization present
a natural and significant test. I will argue that modern
nonsmooth analysis passes this test with distinction.
Boris S. Mordukhovich: Sequential Variational Analysis in Infinite Dimensions
We are going to present a geometric approach to variational analysis in
infinite-dimensional spaces involving sequential generalized differential
constructions for sets, nonsmooth (possible extended-real-valued)
functions, and set-valued mappings. This approach is based on the
so-called extremal principle that provides necessary conditions for set
extremality (of Euler's type) and can be viewed as a variational
counterpart of the classical convex separation principle in nonconvex
settings.
Jean-Paul Penot: Analysis of Value Functions
See the attached ps-file.
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