Algebraic geometry has a long and distinguished presence in the history of mathematics that produced both powerful and elegant theorems. In recent years new algorithms have been developed and this has lead to unexpected and exciting interactions with optimization theory. Particularly noteworthy is the cross-fertilization between Groebner bases and integer programming, and real algebraic geometry and semidefinite programming. The latter includes approaches to polynomial optimization that are based on sums of squares, and new approximation hierarchies for hard combinatorial optimization problems.
This workshop will focus on research directions at the interface of convex optimization and algebraic geometry, with both domains understood in the broadest sense. The problems and algorithms to be discussed arise from fields as diverse as functional analysis, control theory, probability theory, statistics, numerical algebraic geometry, combinatorics, multilinear algebra, and their applications in engineering and the life sciences. Of particular interest will be also the development of computational benchmarks and the integration of numerical optimization software with symbolic algebra packages.
(University of California, San Diego (UCSD))
Monique Laurent (CWI, Amsterdam, and U. Tilburg)
Pablo Parrilo (Massachusetts Institute of Technology)
Bernd Sturmfels (University of California, Berkeley (UC Berkeley))
Rekha Thomas (University of Washington)