Knobloch, Matthias : Solving Convex Programs via Lagrangian Decomposition

Author(s):

Knobloch, Matthias

Title:

Solving Convex Programs via Lagrangian Decomposition

Electronic source:

application/postscript
application/pdf

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 8, 2003

Mathematics Subject Classification:

90C25			[ Convex programming ]
90C30			[ Nonlinear programming ]
65K05			[ Mathematical programming ]

Abstract:

We consider general convex large-scale optimization problems in finite dimensions. Under usual assumptions concerning the structure of the constraint functions, the considered problems are suitable for decomposition approaches. Lagrangian-dual problems are formulated and solved by applying a well-known cutting-plane method of level-type. The proposed method is capable to handle infinite function values. Therefore it is no longer necessary to demand the feasible set with respect to the non-dualized constraints to be bounded. The paper primarily deals with the description of an appropriate oracle. We first discuss the realization of the oracle under requisite assumptions for generic convex problems. Afterwards we show that for convex quadratic programs the algorithm of the oracle is universally applicable. Moreover, a method to construct approximate feasible and approximate optimal, primal solutions is given.

Keywords:

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

Language:

English

Publication time:

9 / 2003