A proximal bundle method with approximate subgradient linearizations. (English) Zbl 1104.65055

Kiwiel, Krzysztof C.

SIAM J. Optim. 16, No. 4, 1007-1023 (2006).

The author studies a proximal bundle method for optimizing a convex function over a closed convex set in Euclidean space. The article begins with a set of useful definitions which are followed by the main contribution of this article namely the inexact proximal bundle method. A proposed algorithm is outlined and several properties of the method are studied in detail, such as convergence, optimality measures and stopping criteria. The article concludes with a list of useful references.

Reviewer: Efstratios Rappos (Athens)

MSC:

65K05	Numerical mathematical programming methods
90C25	Convex programming

Keywords:

nondifferentiable optimization; convex programming; approximate subgradients; proximal bundle methods; algorithm