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

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