Necessary and sufficient conditions for interval‐valued differentiability

This work is included in the search of optimality conditions for solutions to the scalar interval optimization problem, both constrained and unconstrained, by means of second-order optimality conditions. As it is known, these conditions allow us to reject some candidates to minima that arise from the first-order conditions. We will define new concepts such as second-order gH-derivative for interval-valued functions, 2-critical points, and 2-KKT-critical points. We obtain and present new types of interval-valued functions, such as 2-pseudoinvex, characterized by the property that all their second-order stationary points are global minima. We extend the optimality criteria to the semi-infinite programming problem and obtain duality theorems. These results represent an improvement in the treatment of optimization problems with interval-valued functions.

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Necessary and sufficient conditions for interval‐valued differentiability

Cited by 3 publications

References 30 publications

Gradient-based descent linesearch to solve interval-valued optimization problems under gH-differentiability with application to finance

Gradient-based descent linesearch to solve interval-valued optimization problems under gH-differentiability with application to finance

Characterization results of generalized differentiabilities of fuzzy functions

Second-order optimality conditions for interval-valued functions

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