Beer, Klaus ; Knobloch, Matthias : Utilization of the Level Method for Dual Decomposition in Convex Quadratic Programming

Author(s):

Beer, Klaus
Knobloch, Matthias

Title:

Utilization of the Level Method for Dual Decomposition in Convex Quadratic Programming

Electronic source:

application/postscript

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 4, 2002

Mathematics Subject Classification:

90C25			[ Convex programming ]
90C20			[ Quadratic programming ]

Abstract:

We describe a method, which enables us to solve optimization problems resulting from dual decomposition approaches. We make use of a well-known cutting plane method of level-type. This method allows us, to get rid of the compactness-condition for the resulting inner problems because the described level method can handle infinite function values. The principal aim of this paper is the description of an appropriate oracle. The case of optimization problems with convex quadratic objective functions and affine-linear constraints is fully exploited and a detailled algorithm is given for the mentioned class of problems. Some numerical tests for problems with exclusively finite function values close the paper. We compare the standard method with a method using normalized subgradients.

Keywords:

level method, decomposition methods, quadratic programming, cutting plane methods, nonsmooth programming

Language:

English

Publication time:

5 / 2002