In this work we present a family of variable metric interior proximal methods for solving optimization problems under nonnegativity constraints. We define two algorithms, in the inexact and exact forms. The kernels are metrics generated by diagonal matrices in each iteration and the regularization parameters are conveniently chosen to force the iterates to be interior points. We show the well definedness of the algorithms and we establish weak convergence to the solution set of the problem.
PESC/COPPE-Federal University of Rio de Janeiro, CP 68511, 21945-970, Rio de Janeiro, RJ, Brazil, 10/2006