2021/04/22 by Gourav Kumar, Debdas Ghosh, Kumar, Gourav +1
Computer Science · Mathematics · #FOS: Mathematics #Fuzzy Systems and Optimization #Optimization and Control (math.OC) #Optimization and Variational Analysis #math.OC
paper · pdf · doi:10.48550/arxiv.2104.11167
arxiv created 2021/04/22 · openalex publication_date 2021/04/22 · arxiv updated 2021/04/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we attempt to propose Ekeland's variational principle for interval-valued functions (IVFs). To develop the variational principle, we study the 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-Gateaux differentiable IVF, the proposed Ekeland's variational principle is used.