PROXIMITY CONTROL IN BUNDLE METHODS FOR CONVEX NONDIFFERENTIABLE MINIMIZATION

Proximal bundle methods for minimizing a convex function f generate a sequence {xk} by taking xk+1 to be the minimizer of {Mathematical expression}, where {Mathematical expression} is a sufficiently accurate polyhedral approximation to f and uk > 0. The usual choice of uk = 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. © 1990 North-Holland.