Global saddle-point duality for quasi-concave programs |
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Authors: | Jacob Flachs |
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Institution: | (1) National Research Institute for Mathematical Sciences of the CSIR, P.O. Box 395, Pretoria, South Africa |
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Abstract: | General and quasi-concave non-differentiable cases of the maximization of the minimun between two functions are considered. With the aid of duality theory for mathematical programming involving conjugate-like operators and by defining a bifunction we construct a new Lagrangian and generate a class of perturbations. New saddle-point theorems are presented, and equivalence is proved between the existence of a saddle-point and the existence of a certain cone-supporting property of the perturbation function. These results suggest possible improvements in multiplier methods.This work was partially supported by a grant from Control Data. |
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Keywords: | Mathematical Programming Convex Functions Quasi-Concave and Quasi-Convex Functions Bifunctions Perturbation Saddle-points Lagrangian |
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