Kiwiel, Krzysztof C. Proximal minimization methods with generalized Bregman functions. (English) Zbl 0890.65061 SIAM J. Control Optimization 35, No. 4, 1142-1168 (1997). 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. Reviewer: K.Schittkowski (Bayreuth) Cited in 2 ReviewsCited in 103 Documents MSC: 65K05 Numerical mathematical programming methods 90C25 Convex programming Keywords:convex programming; nondifferentiable optimization; proximal methods; Bregman functions; \(B\)-functions; convergence; nonquadratic multiplier methods PDFBibTeX XMLCite \textit{K. C. Kiwiel}, SIAM J. Control Optim. 35, No. 4, 1142--1168 (1997; Zbl 0890.65061) Full Text: DOI