k
} by taking xk to be an approximate minimizer of , where is a piecewise linear model of f constructed from accumulated subgradient linearizations of f, Dh is the D-function of a generalized Bregman function h and tk>0. Convergence under implementable criteria is established by extending our recent framework of Bregman proximal minimization, which is of independent interest, e.g., for nonquadratic multiplier methods for constrained minimization. In particular, we provide new insights into the convergence properties of bundle methods based on h=½|·|2.
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Received September 18, 1997 / Revised version received June 30, 1998 Published online November 24, 1998
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Kiwiel, K. A bundle Bregman proximal method for convex nondifferentiable minimization . Math. Program. 85, 241–258 (1999). https://doi.org/10.1007/s101070050056
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DOI: https://doi.org/10.1007/s101070050056