Purpose of the Workshop
The aim of the Workshop is to review and discuss recent developments of the theory of Convex Analysis and Optimization
and to provide a forum for fruitful interactions in closely related fields of research and their applications.
Optimization is a rich and thriving mathematical discipline.
Properties of minimizers and maximizers of functions rely in an essential way on richness of techniques from mathematical
analysis, including tools from calculus and its generalizations, topology, and geometry. The theory underlying current computational
optimization techniques grows evermore: sophisticated duality-based algorithms, interior point methods, and control-theoretic applications are typical examples. The powerful and elegant language of convex analysis unifies much of this theory.
Many important analytic problems have illuminating optimization formulations and hence can be approached through main variational tools: subgradients and optimality conditions, the many forms of duality, metric regularity and so forth. More generally, the idea of convexity is central to the transition from classical analysis to various branches of modern analysis: from linear to nonlinear analysis, from smooth to nonsmooth, from the study of functions to multifunctions and has important applications in optimal control, mathematical economics, and other areas of infinite-dimensional optimization.
Particular emphasis will be placed on novel ideas and promising research developments.
Specific topics of interest are (but not limited to):
- Nonlinear Optimization
- Stochastic Optimization
- Variational Inequalities
- Differential Inclusions
- Differential Variational Inequalities
- Optimization for Imaging
- Optimization for Finance
- Optimal Transportation Theory
- Optimization for Machine Learning
- Convex, Nonsmooth and Energy Optimization
- Optimization and Dynamical Systems
- Equilibrium Problems
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