Currently displaying 1 – 2 of 2

Showing per page

Order by Relevance | Title | Year of publication

Inertias and ranks of some Hermitian matrix functions with applications

Xiang Zhang;  Qing-Wen Wang;  Xin Liu — 2012

Open Mathematics

Let S be a given set consisting of some Hermitian matrices with the same size. We say that a matrix A ∈ S is maximal if A − W is positive semidefinite for every matrix W ∈ S. In this paper, we consider the maximal and minimal inertias and ranks of the Hermitian matrix function f(X,Y) = P − QXQ* − TYT*, where * means the conjugate and transpose of a matrix, P = P*, Q, T are known matrices and for X and Y Hermitian solutions to the consistent matrix equations AX =B and YC = D respectively. As applications,...

Convergence analysis of adaptive trust region methods

Zhen-Jun Shi;  Xiang-Sun Zhang;  Jie Shen — 2007

RAIRO - Operations Research

In this paper, we propose a new class of adaptive trust region methods for unconstrained optimization problems and develop some convergence properties. In the new algorithms, we use the current iterative information to define a suitable initial trust region radius at each iteration. The initial trust region radius is more reasonable in the sense that the trust region model and the objective function are more consistent at the current iterate. The global convergence, super-linear and quadratic convergence...

Page 1

Download Results (CSV)