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Proximity control in bundle methods for convex nondifferentiable minimization

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Abstract

Proximal bundle methods for minimizing a convex functionf generate a sequence {x k} by takingx k+1 to be the minimizer of\(\hat f^k (x) + u^k |x - x^k |^2 /2\), where\(\hat f^k \) is a sufficiently accurate polyhedral approximation tof andu k > 0. The usual choice ofu k = 1 may yield very slow convergence. A technique is given for choosing {u k} adaptively that eliminates sensitivity to objective scaling. Some encouraging numerical experience is reported.

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This research was supported by Project CPBP.02.15.

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Kiwiel, K.C. Proximity control in bundle methods for convex nondifferentiable minimization. Mathematical Programming 46, 105–122 (1990). https://doi.org/10.1007/BF01585731

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  • DOI: https://doi.org/10.1007/BF01585731

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