Unger, Thomas : A Modified Version of the Level Method Applicable for Decomposition

Author(s) :

Unger, Thomas

Title :

A Modified Version of the Level Method Applicable for Decomposition

Preprint series

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 2000-01, 2000

Mathematics Subject Classification :

90C25 [ Convex programming ]

65K05 [ Mathematical programming (numerical methods) ]

Abstract :

In this paper we describe a version of the level method for solving a nondifferentiable program where the problem data (feasible set, functionvalues, and subgradients) are not known explicitely and may be computed using an oracle only up to a appropriately chosen accuracy eps We show that the modified level method produces a delta^{dom}-feasible, delta^{opt}-optimal solution after a finite number of oracle calls for positive delta^{dom}, delta^{opt}. Further, we describe how our general algorithm can be applied to decomposition problems which are generally nondifferentiable. In such an application the assumption of eps-exact data is natural since the inner program of the decomposed problem in general is nonlinear and hence solvable only approximately.

Keywords :

nondifferentiable optimization, convex optimization, level method, cutting plane method, inexact data, decomposition

Language :

english

Publication time :

1/2000