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Zbl 0890.65061
Kiwiel, Krzysztof C.
Proximal minimization methods with generalized Bregman functions. (English)
[J] SIAM J. Control Optimization 35, No.4, 1142-1168 (1997). ISSN 0363-0129; ISSN 1095-7138/e

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.
[K.Schittkowski (Bayreuth)]

MSC 2000:: *65K05 Mathematical programming (numerical methods)
90C25 Convex programming

Keywords: convex programming; nondifferentiable optimization; proximal methods; Bregman functions; $B$-functions; convergence; nonquadratic multiplier methods

Cited in: Zbl 1208.65080 Zbl 0955.90101

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