Friday, 11:00 - 11:25 h, Room: H 2036

 

Sabine Burgdorf
Lasserre relaxation for trace-optimization of NC polynomials

Coauthors: Kristijan Cafuta, Igor Klep, Janez Povh

 

Abstract:
Given a polynomial f in noncommuting (NC) variables, what is the smallest trace f(A) can attain for a tuple A of symmetric matrices? This is a nontrivial extension of minimizing a polynomial in commuting variables or of eigenvalue optimization of an NC polynomial - two topics with various applications in several fields. We propose a sum of Hermitian squares relaxation for trace-minimization of an NC polynomial and its implementation as an SDP. We will discuss the current state of knowledge about this relaxation and compare it to the behavior of Lasserre relaxations for classical polynomial minimization and for eigenvalue optimization respectively.

 

Talk 2 of the invited session Fri.1.H 2036
"Algebraic geometry and conic programming I" [...]
Cluster 4
"Conic programming" [...]

 

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