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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.
Krzysztof C. Kiwiel (Tue,) studied this question.
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