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arXiv · 2308.01914

Fritz-John optimality condition in fuzzy optimization problems and its application to classification of fuzzy data

Fangfang Shi·Guoju Ye·Wei Liu·Debdas Ghosh
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Abstract

The main objective of this paper is to derive the optimality conditions for one type of fuzzy optimization problems. At the beginning, we define a cone of descent direction for fuzzy optimization, and prove that its intersection with the cone of feasible directions at an optimal point is an empty set. Then, we present first-order optimality conditions for fuzzy optimization problems. Furthermore, we generalize the Gordan's theorem for fuzzy linear inequality systems and utilize it to deduce the Fritz-John optimality condition for the fuzzy optimization with inequality constraints. Finally, we apply the optimality conditions established in this paper to a binary classification problem for support vector machines with fuzzy data. In the meantime, numerical examples are described to demonstrate the primary findings proposed in the present paper.

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Fangfang Shi, Guoju Ye, Wei Liu, Debdas Ghosh. 2023-07-05. Fritz-John optimality condition in fuzzy optimization problems and its application to classification of fuzzy data. https://arxiv.org/abs/2308.01914

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