The paper aims to provide a necessary and sufficient condition for global maximum points for a real valued function by the notion of invisible points. The use of invisible points with respect to a function for optimization is suggested by the tight link between invisible points and monotonicity: it allows to reinterpret the set of global maximum points of a function as the set of those points which are not invisible with respect to it. This approach is valid for both one variable and several variables functions, allowing, in this second case, to consider different orders in the domain. Moreover, optimization problems with constraints may be analyzed following such a approach: few interesting considerations might be conducted for reinterpreting classical economic problems according to the proposed viewpoint.
Invisible points and optimization
BECCACECE, FRANCESCA;CIGOLA, MARGHERITA
1998
Abstract
The paper aims to provide a necessary and sufficient condition for global maximum points for a real valued function by the notion of invisible points. The use of invisible points with respect to a function for optimization is suggested by the tight link between invisible points and monotonicity: it allows to reinterpret the set of global maximum points of a function as the set of those points which are not invisible with respect to it. This approach is valid for both one variable and several variables functions, allowing, in this second case, to consider different orders in the domain. Moreover, optimization problems with constraints may be analyzed following such a approach: few interesting considerations might be conducted for reinterpreting classical economic problems according to the proposed viewpoint.
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