# Solving convex program via Lagrangian decomposition

Kybernetika (2004)

- Volume: 40, Issue: 5, page [595]-610
- ISSN: 0023-5954

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topKnobloch, Matthias. "Solving convex program via Lagrangian decomposition." Kybernetika 40.5 (2004): [595]-610. <http://eudml.org/doc/33722>.

@article{Knobloch2004,

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 appropriate assumptions for generic convex problems. Afterwards we show that for convex quadratic programs the algorithm of the oracle is universally applicable.},

author = {Knobloch, Matthias},

journal = {Kybernetika},

keywords = {level method; cutting-plane methods; decomposition methods; convex programming; nonsmooth programming; level method; cutting-plane method; decomposition method; nonsmooth programming},

language = {eng},

number = {5},

pages = {[595]-610},

publisher = {Institute of Information Theory and Automation AS CR},

title = {Solving convex program via Lagrangian decomposition},

url = {http://eudml.org/doc/33722},

volume = {40},

year = {2004},

}

TY - JOUR

AU - Knobloch, Matthias

TI - Solving convex program via Lagrangian decomposition

JO - Kybernetika

PY - 2004

PB - Institute of Information Theory and Automation AS CR

VL - 40

IS - 5

SP - [595]

EP - 610

AB - 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 appropriate assumptions for generic convex problems. Afterwards we show that for convex quadratic programs the algorithm of the oracle is universally applicable.

LA - eng

KW - level method; cutting-plane methods; decomposition methods; convex programming; nonsmooth programming; level method; cutting-plane method; decomposition method; nonsmooth programming

UR - http://eudml.org/doc/33722

ER -

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