Title :
Nonsmooth Newton´s method for positive semi definite solution of nonlinear matrix equations
Author :
Benahmed, Boubakeur ; Nachi, Khadra ; Yassine, Abdulsalam
Author_Institution :
Dept. of Math. & Comput. Sci., ENSET of Oran, El M´naouer, Algeria
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 semi-definite cone of matrices, the conic constrained equation is transformed to a nonsmooth unconstrained equation which is solved by the nonsmooth Newton´s method. Here, we use an explicit expression of the Clarke generalized 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 superlinearly (respectively, quadratically).
Keywords :
Jacobian matrices; Newton method; mathematical programming; nonlinear equations; Clarke generalized Jacobian; conic constrained equation; conic constrained nonlinear matrix equations; nonsmooth Newton method; nonsmooth unconstrained equation; orthogonal projection; positive semi definite solution; positive semi-definite cone of matrices; positive semidefinite matrices; Convergence; Equations; Jacobian matrices; Newton method; Sun; Symmetric matrices; Tin;
Conference_Titel :
Modeling, Simulation and Applied Optimization (ICMSAO), 2013 5th International Conference on
Conference_Location :
Hammamet
Print_ISBN :
978-1-4673-5812-5
DOI :
10.1109/ICMSAO.2013.6552564