## 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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Author: A. Winterfeld urn:nbn:de:hbz:386-kluedo-14342 Berichte des Fraunhofer-Instituts für Techno- und Wirtschaftsmathematik (ITWM Report) (91) Report English 2006 2006 Fraunhofer-Institut für Techno- und Wirtschaftsmathematik Fraunhofer ITWM 2006/06/08 clustering; design centering; general semi-infinite optimization; large scale optimization; nonlinear programmingclustering; design centering; general semi-infinite optimization; large scale optimization; nonlinear programming Fraunhofer (ITWM) 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

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