Proximal Minimization Methods with Generalized Bregman Functions

We consider methods for minimizing a convex function f that generate a sequence fx k g by taking x k+1 to be an approximate minimizer of f(x) +D h (x; x k )=c k , where c k ? 0 and D h is the D-function of a Bregman function h. Extensions are made to B-functions that generalize Bregman functions and cover more applications. Convergence is established under criteria amenable to implementation. Applications are made to nonquadratic multiplier methods for nonlinear programs