Proximal Minimization Methods with Generalized Bregman Functions

We consider methods for minimizing a convex function f that generate a sequence xk by taking xk+1 to be an approximate minimizer of f (x) +Dh (x, xk) /ck, where ck > 0 and Dh 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.