Proximal Minimization Methods with Generalized Bregman Functions

Abstract

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.