| Day | Time | Type | Place | Note |
|---|---|---|---|---|
| Tuesday | 3:30 PM - 5:30 PM | lesson | Lecture Hall M | from Oct 18, 2011 to Jan 31, 2012 |
| Friday | 3:30 PM - 5:30 PM | lesson | Lecture Hall M | from Oct 21, 2011 to Jan 31, 2012 |
In this course we will provide an introduction to Convex Analysis in finite and infinite-dimensional spaces. We will show also some applications to problems of nonlinear optimizations and control theory arising from physics and economics.
Review of weak topology on Banach spaces: convex sets, Minkowski functional, linear continuous operators, weak topology, separation of convex sets.
Convex functions: general properties, lower semicontinuous convex functions, convex conjugate, subdifferential in the sense of Convex Analysis. Introduction to Calculus of Variations.
Generalizations of convexity: differential calculus in Hilbert and Banach spaces, proximal and limiting subdifferential, the density theorem, sum rule, chain rule, generalized gradient in Banach space.
Introduction to control theory: multifunctions and trajectories of differential inclusions, viability,
equilibria, invariance, stabilization, reachability, Pontryagin Maximum Principle, necessary conditions
for optimality.
Application to optimization problems arising from physical or economic models.
| Author | Title | Publisher | Year | ISBN | Note |
| Ivar Ekeland and Roger Témam | Convex Analysis and Variational Problems | SIAM | 1987 | 0-89871-450-8 | |
| F.H. Clarke, Y.S. Ledyaev, Ronald J. Stern, P.R. Wolenski | Nonsmooth Analysis and Control Theory | Springer-Verlag New York Inc. | 1998 | 0387983368 | |
| Frank H. Clarke | Optimization and Nonsmooth Analysis | SIAM | 1990 | 0-89871-256-4 |
Written and oral examination. There will be also two partial tests during the course.
