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Proximal Minimization Methods with Generalized Bregman Functions


  • K. Kiwiel


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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  • K. Kiwiel, 1995. "Proximal Minimization Methods with Generalized Bregman Functions," Working Papers wp95024, International Institute for Applied Systems Analysis.
  • Handle: RePEc:wop:iasawp:wp95024

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    1. K. Kiwiel, 1994. "Free-Steering Relaxation Methods for Problems with Strictly Convex Costs and Linear Constraints," Working Papers wp94089, International Institute for Applied Systems Analysis.
    2. Jong-Il Kim & Lawrence J. Lau, 1996. "The sources of Asian Pacific economic growth," Canadian Journal of Economics, Canadian Economics Association, vol. 29(s1), pages 448-454, April.
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