Ekeland’s variational principle for interval-valued functions

In this paper, we attempt to propose Ekeland’s variational principle for interval-valued functions (IVFs). To develop the variational principle, we study a concept of sequence of intervals. In the sequel, the idea of gH -semicontinuity for IVFs is explored. A necessary and sufficient condition for a...

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Bibliographic Details
Published in:Computational & applied mathematics 2023-02, Vol.42 (1), Article 28
Main Authors: Kumar, Gourav, Ghosh, Debdas
Format: Article
Language:English
Subjects:
Applications of Mathematics
Applied physics
Computational mathematics
Computational Mathematics and Numerical Analysis
Mathematical Applications in Computer Science
Mathematical Applications in the Physical Sciences
Mathematics
Mathematics and Statistics
Principles
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Summary:In this paper, we attempt to propose Ekeland’s variational principle for interval-valued functions (IVFs). To develop the variational principle, we study a concept of sequence of intervals. In the sequel, the idea of gH -semicontinuity for IVFs is explored. A necessary and sufficient condition for an IVF to be gH -continuous in terms of gH -lower and upper semicontinuity is given. Moreover, we prove a characterization for gH -lower semicontinuity by the level sets of the IVF. With the help of this characterization result, we ensure the existence of a minimum for an extended gH -lower semicontinuous, level-bounded and proper IVF. To find an approximate minima of a gH -lower semicontinuous and gH -Gâteaux differentiable IVF, the proposed Ekeland’s variational principle is used.
ISSN:2238-3603
1807-0302
DOI:10.1007/s40314-022-02173-x