**INTERNATIONAL
SCHOOL OF MATHEMATICS "GUIDO STAMPACCHIA"**

**ERICE - SICILY:
24 June - 1 July, 2019**

- Nonsmooth, stochastic and
convex optimization

- Variational inequalities and differential inclusions

- Optimization and control of
dynamical systems

- Equilibrium problems

- Nonsmooth and variational analysis

- Optimization for imaging

- Finance and machine learning

- Energy optimization

- Computational mathematical programming and optimization algorithms

**PURPOSE
OF THE WORKSHOP**

The aim of the Workshop is to review and discuss recent developments of 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 Strong smoothness requirements, that were present in the early theory, have lately been replaced by weaker notions of differentiability, which are more natural in applications.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.