Séminaire Boubakeur Benhamed

Jeudi 14 Mars 2013 (14h00 (salle G001))

Boubakeur BENAHMED, Ecole Nationale polytechnique d'Oran, Algérie.

Titre : Nonsmooth singular Newton's method for positive semi definite solution of nonlinear matrix equations.

Résumé : In this work, we propose a new method for solving conic constrained nonlinear matrix equations. With the use of the orthogonal projection onto the positive cone of matrices, the conic constrained equation is transformed to a nonsmooth singular unconstrained equation

which is solved by the nonsmooth version of Newton's method. Here, we use an explicit expression of the Clarke generalized Jacobian of the orthogonal projection as developed by several authors. We prove under natural assumptions that the proposed method converges locally superlinearly (respectively, quadratically).