1751
eng
2829
2843
439
reportzib
0
2012-12-20
2012-12-20
--
On the semidefinite representations of real functions applied to symmetric matrices
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.
1438-0064
urn:nbn:de:0297-zib-17511
10.1016/j.laa.2013.08.021
Appear in: Linear Algebra and its Applications
Guillaume Sagnol
Guillaume Sagnol
ZIB-Report
12-50
eng
uncontrolled
semidefinite representability
eng
uncontrolled
optimal experimental designs
eng
uncontrolled
SDP
eng
uncontrolled
matrix geometric mean
Mathematics of Computing
OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING
Mathematical Optimization
Sagnol, Guillaume
https://opus4.kobv.de/opus4-zib/files/1751/ZR-12-50.pdf
https://opus4.kobv.de/opus4-zib/files/1751/ZR-12-50revised.pdf
https://opus4.kobv.de/opus4-zib/files/1751/sdp_ratpow_zib_final-1.pdf