Abstract
The aim of this paper is to study the class of maximization problems having linear constraints and an objective function given by the product of an affine function raised to a certain power and another affine function. For such a class of problems, several theoretical aspects are investigated: values of the exponent for which there exists a finite optimum for any feasible region, conditions implying a finite supremum, conditions which ensure that a local maximum is a global maximum, optimality conditions with respect to a vertex of the feasible region, and so on. The obtained results allow us to suggest, for any exponent, a sequential simplex-like method converging to a global optimal solution in a finite number of steps. This algorithm reduces with the one given by Cambini and Martein [3, 5] for the linear fractional case.
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© 1994 Springer-Verlag Berlin Heidelberg
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Cambini, R. (1994). A class of non-linear programs: theoretical and algorithmical results. In: Komlósi, S., Rapcsák, T., Schaible, S. (eds) Generalized Convexity. Lecture Notes in Economics and Mathematical Systems, vol 405. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46802-5_23
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DOI: https://doi.org/10.1007/978-3-642-46802-5_23
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