Quadratic geometric programming with application to machining economics.

*(English)*Zbl 0558.90074Geometric Programming is extended to include convex quadratic functions. Generalized Geometric Programming is applied to this class of programs to obtain a convex dual program. Machining economics problems fall into this class. Such problems are studied by applying this duality to a nested set of three problems. One problem is zero degree of difficulty and the solution is obtained by solving a simple system of equations. The inclusion of a constraint restricting the force on the tool to be less than or equal to the breaking force provides a more realistic solution. This model is solved as a program with one degree of difficulty. Finally the behavior of the machining cost per part is studied parametrically as a function of axial depth.

##### MSC:

90C25 | Convex programming |

90C99 | Mathematical programming |

90B30 | Production models |

90C20 | Quadratic programming |

49N15 | Duality theory (optimization) |

90C55 | Methods of successive quadratic programming type |

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\textit{T. R. Jefferson} and \textit{C. H. Scott}, Math. Program. 31, 137--152 (1985; Zbl 0558.90074)

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##### References:

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