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Mathematical Programming

, Volume 46, Issue 1–3, pp 105–122 | Cite as

Proximity control in bundle methods for convex nondifferentiable minimization

  • Krzysztof C. Kiwiel
Article

Abstract

Proximal bundle methods for minimizing a convex functionf generate a sequence {x k } by takingxk+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.

Key words

Nondifferentiable minimization convex programming numerical methods descent methods 

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Copyright information

© North-Holland 1990

Authors and Affiliations

  • Krzysztof C. Kiwiel
    • 1
  1. 1.Systems Research InstitutePolish Academy of SciencesWarsawPoland

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