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Erschienen in:
1996 | OriginalPaper | Buchkapitel
Nonconvex Global Optimization of the Separable Resource Allocation Problem with Continuous Variables
verfasst von : Emile Haddad
Erschienen in: State of the Art in Global Optimization
Verlag: Springer US
Enthalten in: Professional Book Archive
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New results are presented for solving the well-known nonlinear programming problem: Minimize F= ∑ fi(xi) subject to ∑ xi=r and xi ≥ 0; which has been studied over the past thirty years in numerous application areas. Whereas current solution methods are restricted to convex fi(xi), the new results allow the functions fi(xi) to be nonconvex and multimodal with any number of maxima and minima over [0, X]. Necessary conditions for the local minima of F(x1, x2,… xn) are derived. The necessary conditions for local minima are used to determine a superset M of the set of all local minima. Minimization of the objective function F over M leads to the global minimum. The results are used to solve examples which no other analytical criteria can solve.