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Erschienen in:
1988 | OriginalPaper | Buchkapitel
Linear Complementarity Problems: A Cutting Plane Method Based on the Convex Hull of Polyhedra
verfasst von : V. De Angelis
Erschienen in: Structural Optimization
Verlag: Springer Netherlands
Enthalten in: Professional Book Archive
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Some structural engineering issues leading to linear complementarity problems (l.c.p.) are presented. Then the set of solutions of a linear complementarity system (l.c.s.) is represented as the union of a finite — but, unfortunately, large - number of polyhedra and the l.e.p. is reformulated as the problem of determining a supporting hyperplane of the closure of the convex hull of such union. The supporting hyperplane of any single polyhedron — which is obtained by means of parametric linear programming — generates a cut in the space of parameters, which can be so powerful as to eliminate half of the polyhedra that are to be considered in the resolution of the l.c.p..Besides, the parametric linear programming problem which has to be solved after the introduction of the cut has a smaller dimension.