Mathematical Programming

, Volume 46, Issue 1, pp 105–122

Proximity control in bundle methods for convex nondifferentiable minimization


  • Krzysztof C. Kiwiel
    • Systems Research InstitutePolish Academy of Sciences

DOI: 10.1007/BF01585731

Cite this article as:
Kiwiel, K.C. Mathematical Programming (1990) 46: 105. doi:10.1007/BF01585731


Proximal bundle methods for minimizing a convex functionf generate a sequence {xk} 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 anduk > 0. The usual choice ofuk = 1 may yield very slow convergence. A technique is given for choosing {uk} adaptively that eliminates sensitivity to objective scaling. Some encouraging numerical experience is reported.

Key words

Nondifferentiable minimizationconvex programmingnumerical methodsdescent methods

Copyright information

© North-Holland 1990