Proximal Minimization Methods with Generalized Bregman Functions

Kiwiel, K. (1995). Proximal Minimization Methods with Generalized Bregman Functions. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-95-024

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Abstract

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.

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