Jakub Marecek presents (Semi-)Algebraic Geometry at IBM Research -- Ireland
On 2016-11-22 11:00:00 at G205, Karlovo náměstí 13, Praha 2
Across applications in power systems, water systems, and transportation, one
encounters non-linear physics, which can be expressed or approximated by
polynomials. Both operational and planning problems therein can be studied as
polynomial optimisation problems (POPs), using tools from (semi-)algebraic
geometry.
We present an overview of our recent analytical and computational results. Some
of the most interesting analytical results are based on the work of Bernstein,
Kushnirenko, and Khovanski on mixed volumes. Others employ the alpha-beta theory
of Shub and Smale in switching between solving convexifications and solving the
non-convex Lagrangian using Newton method. Computationally, we employ a variety
of tools, including custom SDP solvers, matrix-completion solvers, SeDuMi, and
Bertini.
encounters non-linear physics, which can be expressed or approximated by
polynomials. Both operational and planning problems therein can be studied as
polynomial optimisation problems (POPs), using tools from (semi-)algebraic
geometry.
We present an overview of our recent analytical and computational results. Some
of the most interesting analytical results are based on the work of Bernstein,
Kushnirenko, and Khovanski on mixed volumes. Others employ the alpha-beta theory
of Shub and Smale in switching between solving convexifications and solving the
non-convex Lagrangian using Newton method. Computationally, we employ a variety
of tools, including custom SDP solvers, matrix-completion solvers, SeDuMi, and
Bertini.