A proximal method with separable Bregman distances for quasiconvex minimization over the nonnegative orthant

We present an interior proximal method with Bregman distance, for solving the minimization problem with quasiconvex objective function under nonnegative constraints. The Bregman function is considered separable and zone coercive, and the zone is the interior of the positive orthant. Under the assumption that the solution set is nonempty and the objective function is continuously differentiable, we establish the well definedness of the sequence generated by our algorithm and obtain two important convergence results, and show in the main one that the sequence converges to a solution point of the problem when the regularization parameters go to zero.