2021/04/15 by Amit Kumar Debnath, Debdas Ghosh, Debnath, Amit Kumar +5
Computer Science · Decision Sciences · Mathematics · #FOS: Mathematics #Fuzzy Systems and Optimization #Multi-Criteria Decision Making #Optimization and Control (math.OC) #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.2104.07497
openalex publication_date 2021/04/15 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
In this article, the concepts of gH-subgradients and gH-subdifferentials of interval-valued functions are illustrated. Several important characteristics of the gH-subdifferential of a convex interval-valued function, e.g., closeness, boundedness, chain rule, etc. are studied. Alongside, we prove that gH-subdifferential of a gH-differentiable convex interval-valued function only contains gH-gradient of that interval-valued function. It is observed that the gH-directional derivative of a convex interval-valued function in each direction is maximum of all the products of gH-subgradients and the direction. Importantly, we show that a convex interval-valued function is gH-Lipschitz continuous if it has gH-subgradients at each point in its domain. Furthermore, the relations between efficient solutions of an optimization problem with interval-valued function and its gH-subgradients are derived.