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Knobloch, Matthias : On Solving Dual Problems with Possible -∞ Function Values Using the Level Method

Knobloch, Matthias : On Solving Dual Problems with Possible -∞ Function Values Using the Level Method

Author(s):
Knobloch, Matthias
Title:
On Solving Dual Problems with Possible -∞ Function Values Using the Level Method
Preprint series:
Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 13, 2004
Mathematics Subject Classification:
90C25 [ Convex programming ]
90C30 [ Nonlinear programming ]
65K05 [ Mathematical programming ]
Abstract:
We describe a method for solving convex optimization problems which usually appear in Lagrangian decomposition approaches. The suggested cutting plane method is capable to handle infinite objective function values and demands an oracle to be given. Some questions of realizing the oracle are discussed. The convergence proof of the level method uses a restrictive condition. We show the essentiality of this condition by example. Moreover, we present a strategy to adjust the problems such that they meet all requirements of the level method. This strategy involves perturbation of the original problem. Finally, we present numerical results, which demonstrate the effectivity of the perturbation approach.
Keywords:
level method, cutting plane methods, decomposition methods, convex programming, nonsmooth programming
Language:
English
Publication time:
8 / 2004