Proximal minimization methods with generalized Bregman functions

We consider methods for minimizing a convex function f that generate a sequence {x(k)} 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.