Prof. Dr. Jesus De Loera (UC Davis, USA)
John-von-Neumann-Professor SS 2013
"Algebraic and Geometric Techniques for Optimization"
- Optimization is a vibrant growing area of Applied Mathematics. Its many successful applications depend on efficient algorithms and this has pushed the development of theory and software. In recent years there has been a resurgence of interest to use ``non-standard'' techniques to estimate the complexity of computation and to guide algorithm design. New interactions with fields like algebraic geometry, representation theory, number theory, combinatorial topology, algebraic combinatorics, and convex analysis have contributed non-trivially to the foundations of computational optimization. This course will be an introduction to the new techniques used in Optimization that have foundation in algebra (number theory, commutative algebra, real algebraic geometry, representation theory) and geometry (convex and differential geometry, combinatorial topology, algebraic topology, etc).
- In these introductory lectures I will present these new approaches to all senior students. Topics to be included are: Convex and linear optimization (topological tools for on the simplex method, differential geometry and curvature for the central paths of interior point methods), Integer programming and Combinatorial optimization (Graver bases, Generating functions, Nullstellensatz for combinatorial problems), Nonlinear Global Optimization (sum of square methods, semidefinite programming, compressed sensing, cone programming and hyperbolic geometry).
- You find more details about the lecture on the homepage Algebraic and Geometric Techniques for Optimization.