Add to ORKGAbstract A real-valued continuous function on an interval gives rise to a map via functional calculus from the convex set of Hermitian matrices all of whose eigenvalues belong to the interval. Since the subpace of Hermitian matrices is provided with the order structure induced by the cone of positive semidefinite matrices, one can consider convexity of this map. We will characterize its convexity by the following trace-inequalities: for . A related topic will be also discussed.</p
Abstract. There is growing interest in optimization problems with real symmetric matrices as variabl...
We prove that a real-valued function f defined on an interval S in R is matrix convex if and only if...
We prove that a real-valued function f defined on an interval S in R is matrix convex if and only if...
A real-valued continuous function f(t) on an interval (α,β) gives rise to a map X!...
Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any m...
In this paper, we prove the convexity of trace functionals (A,B,C)↦Tr|BpACq|s, for parameters (p, q,...
AbstractLet I, J be intervals such that 0 ∈ I ∩ J. Let Mm be the algebra of all m ×m complex matrice...
A stronger version of matrix convexity, called hyperconvexity is introduced. It is shown that the f...
AbstractSome trace inequalities for Hermitian matrices and matrix products involving Hermitian matri...
There is growing interest in optimization problems with real symmetric matrices as variables. Genera...
Abstract. The classical Hermite-Hadamard inequality characterizes the continuous convex func-tions o...
Let f be a real-valued function on [0, ∞) with f(0) = 0 and n be a natural number greater than 1. We...
Let f be a real-valued function on [0, ∞) with f(0) = 0 and n be a natural number greater than 1. We...
AbstractWe prove that the function (x1,…,xk)→Tr(f(x1,…,xk)), defined on k-tuples of symmetric matric...
Let f be a real-valued function on [0, ∞) with f(0) = 0 and n be a natural number greater than 1. We...
Abstract. There is growing interest in optimization problems with real symmetric matrices as variabl...
We prove that a real-valued function f defined on an interval S in R is matrix convex if and only if...
We prove that a real-valued function f defined on an interval S in R is matrix convex if and only if...
A real-valued continuous function f(t) on an interval (α,β) gives rise to a map X!...
Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any m...
In this paper, we prove the convexity of trace functionals (A,B,C)↦Tr|BpACq|s, for parameters (p, q,...
AbstractLet I, J be intervals such that 0 ∈ I ∩ J. Let Mm be the algebra of all m ×m complex matrice...
A stronger version of matrix convexity, called hyperconvexity is introduced. It is shown that the f...
AbstractSome trace inequalities for Hermitian matrices and matrix products involving Hermitian matri...
There is growing interest in optimization problems with real symmetric matrices as variables. Genera...
Abstract. The classical Hermite-Hadamard inequality characterizes the continuous convex func-tions o...
Let f be a real-valued function on [0, ∞) with f(0) = 0 and n be a natural number greater than 1. We...
Let f be a real-valued function on [0, ∞) with f(0) = 0 and n be a natural number greater than 1. We...
AbstractWe prove that the function (x1,…,xk)→Tr(f(x1,…,xk)), defined on k-tuples of symmetric matric...
Let f be a real-valued function on [0, ∞) with f(0) = 0 and n be a natural number greater than 1. We...
Abstract. There is growing interest in optimization problems with real symmetric matrices as variabl...
We prove that a real-valued function f defined on an interval S in R is matrix convex if and only if...
We prove that a real-valued function f defined on an interval S in R is matrix convex if and only if...