کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4599970 | 1336830 | 2013 | 15 صفحه PDF | دانلود رایگان |

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 (or concave) 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 a Riemannian metric over the set of positive definite matrices that for a rational exponent p in the interval (0,1](0,1], the matrix X raised to p is the largest element of a set represented by linear matrix inequalities. This result further generalizes to the case of the matrix A♯pB, which is the point of coordinate p on the geodesic from A to B. We give numerical results for a problem inspired from the theory of experimental designs, which show that the new semidefinite programming formulation can yield an important speed-up factor.
Journal: Linear Algebra and its Applications - Volume 439, Issue 10, 15 November 2013, Pages 2829–2843