Symmetry reduction for Sum-of-Squares programming
2021-07-28, 16:30–17:00 (UTC), JuMP Track

In this talk we discuss a symmetry reduction approach relying on the invariance of the polynomial under a group of actions. From the algebraic properties of the group, the SymbolicWedderburn package determines a change of basis that enables the decomposition of the constraints into smaller bases, some of them being equal which further reduces the problem. We show how to specify the group symmetry to allow SumOfSquares to perform this reformulation automatically.

Sum-of-Squares or semidefinite programming allows to provide guaranteed bounds on remarkably many problems. Although several efficient algorithms exist to solve these programs, their space and time complexity and even their numerical robustness do not scale well with the size of the polynomial basis or semidefinite matrix. To alleviate this problem different methods have been developed to reduce constraints with a large basis or matrix into smaller ones.
These exploit sign symmetry or sparsity structure using chordal decomposition.

Benoît Legat is a postdoctoral associate at MIT with Prof. Pablo Parrilo
in the Laboratory for Information and Decision Systems (LIDS).
He received his Ph.D. degree in applied mathematics from the UCLouvain, Belgium, in 2020.
His research interests include mathematical optimization, invariant set computation and
optimal control.

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I'm a mathematician, researcher in geometric group theory at KIT (Karlsruhe, Germany); I received my PhD in pure mathematics in 2014 and since then changed my scientific focus to aspects including more computational problems. I've been coding in julia since 2016, mostly around group theory, mathematical optimization and certified computation.