An algorithm for nonsmooth convex minimization with errors. (English) Zbl 0584.65034

Kiwiel, Krzysztof C.

Math. Comput. 45, 173-180 (1985).

Author’s summary: A readily implementable algorithm is given for minimizing any convex, not necessarily differentiable, function f of several variables. At each iteration the method requires only one approximate evaluation of f and its \(\epsilon\)-subgradient, and finds a search direction by solving a small quadratic programming problem. The algorithm generates a minimizing sequence of points, which converges to a solution whenever f has any minimizers.

Reviewer: I.H.Mufti

MSC:

65K05	Numerical mathematical programming methods
90C25	Convex programming

Keywords:

nonsmooth convex minimization; descent methods; aggregate subgradients; iteration