Application of general semi-infinite Programming to Lapidary Cutting Problems

  • We consider a volume maximization problem arising in gemstone cutting industry. The problem is formulated as a general semi-infinite program (GSIP) and solved using an interiorpoint method developed by Stein. It is shown, that the convexity assumption needed for the convergence of the algorithm can be satisfied by appropriate modelling. Clustering techniques are used to reduce the number of container constraints, which is necessary to make the subproblems practically tractable. An iterative process consisting of GSIP optimization and adaptive refinement steps is then employed to obtain an optimal solution which is also feasible for the original problem. Some numerical results based on realworld data are also presented.

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Metadaten
Author:A. Winterfeld
URN (permanent link):urn:nbn:de:hbz:386-kluedo-14342
Serie (Series number):Berichte des Fraunhofer-Instituts für Techno- und Wirtschaftsmathematik (ITWM Report) (91)
Document Type:Report
Language of publication:English
Year of Completion:2006
Year of Publication:2006
Publishing Institute:Fraunhofer-Institut für Techno- und Wirtschaftsmathematik
Creating Corporation:Fraunhofer ITWM
Tag:clustering; design centering; general semi-infinite optimization; large scale optimization; nonlinear programming
clustering; design centering; general semi-infinite optimization; large scale optimization; nonlinear programming
Faculties / Organisational entities:Fraunhofer (ITWM)
DDC-Cassification:510 Mathematik

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