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Proximal minimization methods with generalized Bregman functions. (English) Zbl 0890.65061
Author’s 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.

65K05Mathematical programming (numerical methods)
90C25Convex programming
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