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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.

MSC:

65K05 Numerical mathematical programming methods
90C25 Convex programming
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