Non-smooth singular Newton's method for positive semidefinite solution of nonlinear matrix equations Online publication date: Tue, 02-Aug-2016
by Boubakeur Benahmed; Khadra Nachi; Adnan Yassine
International Journal of Operational Research (IJOR), Vol. 27, No. 1/2, 2016
Abstract: In this paper, we propose a new method for solving conic constrained nonlinear matrix equations. With the use of the orthogonal projection onto the positive semidefinite cone of matrices, the conic constrained equation is transformed to a non-smooth unconstrained equation which is solved by the non-smooth Newton's method. Here, we use an explicit expression of the Clarke generalised Jacobian of the projection onto the cone of positive semidefinite matrices as developed by several authors. We prove under natural assumptions that the method converges locally and superlinearly.
Online publication date: Tue, 02-Aug-2016
If you are not a subscriber and you just want to read the full contents of this article, buy online access here.Complimentary Subscribers, Editors or Members of the Editorial Board of the International Journal of Operational Research (IJOR):
Login with your Inderscience username and password:
Want to subscribe?
A subscription gives you complete access to all articles in the current issue, as well as to all articles in the previous three years (where applicable). See our Orders page to subscribe.
If you still need assistance, please email email@example.com