TY - GEN
A1 - Sagnol, Guillaume
T1 - On the semidefinite representations of real functions applied to symmetric matrices
N2 - We present a new semidefinite representation for the trace of
a real function f applied to symmetric matrices, when a
semidefinite representation of the convex function f is known. Our construction
is intuitive, and yields a representation that is more compact than the previously known one.
We also show with the help of matrix geometric means and the Riemannian metric of the set of positive definite matrices
that for a rational number p in the interval (0,1],
the matrix X raised to the exponent p is the largest element
of a set represented by linear matrix inequalities.
We give numerical results for a problem inspired from the theory
of experimental designs, which show that the new semidefinite programming formulation
yields a speed-up factor in the order of 10.
T3 - ZIB-Report - 12-50
KW - semidefinite representability
KW - optimal experimental designs
KW - SDP
KW - matrix geometric mean
Y1 - 2012
UR - https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/1751
UR - https://nbn-resolving.org/urn:nbn:de:0297-zib-17511
SN - 1438-0064
VL - 439
SP - 2829
EP - 2843
ER -