1971 · 15 citations · 1 references
Natural SciencesMathematicsComputational GeometryGeometric ModelingOptimizationCombinatorial OptimizationConstrained OptimizationConvex OptimizationGeometric OptimizationGlobal OptimizationOptimization TheoryConstraintsCutting PlanesNonconvex Optimization
Minimization of a nonconvex objective function subject to linear inequality constraints can involve many local minima. Cutting plane methods for solving such problems have been proposed in the literature. This paper reports computational experience indicating that cutting methods do poorly on problems with dimension as low as ten. A geometric analysis of the conditions involved in cutting a polyhedron shows that:
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