کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4599970 1336830 2013 15 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On the semidefinite representation of real functions applied to symmetric matrices
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
On the semidefinite representation of real functions applied to symmetric matrices
چکیده انگلیسی

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.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 439, Issue 10, 15 November 2013, Pages 2829–2843
نویسندگان
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