International School of Mathematics « Guido Stampacchia » - Workshop Advances in Nonsmooth Analysis and 0ptimization

Monday, June 24, 2019 - 10:15pm to Monday, July 1, 2019 - 10:15pm

The theory of Nonsmooth Analysis and Optimization and to provide a forum for
fruitful interaction in closely related areas. Nonsmooth problems appear in many
fields of applications, such as data mining, image denoising, energy
management, optimal control, neural network training, economics and
computational chemistry and physics. Motivated by these applications
Nonsmooth Analysis has had a considerable impulse that allowed the
development of sophisticated methodologies for solving challenging related
problems. The origin of variational analysis and nonsmooth optimization lies in
the classical calculus of variations and as such is intertwined with the
development of Calculus. Strong smoothness requirements, that were present in
the early theory, have lately been replaced by weaker notions of differentiability,
which are more natural in applications. Nonsmooth optimization is devoted to
the general problem of minimizing functions that are typically not differentiable
at their minimizers. In order to optimize such functions, the classical theory of
optimization cannot be directly used due to lacking certain differentiability and
strong regularity conditions. However, because of the complexity of the real
world, functions used in practical applications are often nonsmooth. Significant
progress in deriving more general optimality conditions for mathematical
programming models has been made in the recent years as a result of advances
in nonsmooth analysis and optimization. The study of nonsmooth problems is
motivated in part by the desire to optimize increasingly sophisticated models of
complex manmade and naturally occurring systems that arise in areas ranging
from economics, operations research, and engineering design to variational
principles that correspond to partial differential equations. Results in nonsmooth
optimization have expedited understanding of the salient aspects of the classic
smooth theory and identified concepts fundamental to optimality that are not
based on differentiability assumptions.

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