Proximal Minimization Methods with Generalized Bregman Functions

K. Kiwiel

Working Papers from International Institute for Applied Systems Analysis

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.

Date: 1995-03
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