Tauheed | Searcharxiv

arXiv2026

Interval-Valued Optimization Problems for Strongly LU-E-Invex and Strongly LU-E-Preinvex Functions

In this paper, we introduce and explore the concepts of strongly LU-E-preinvex (SLUEP), pseudo strongly LU-E-preinvex (PSLUEP) and strongly LU-E-invex (SLUEI) functions. To illustrate and validate these definitions, we provide several non-trivial examples. Additionally, we extend the idea of strongly-G invex sets to the context of interval-valued functions. The epigraph of a SLUEP function is derived, and a relationship between SLUEP and PSLUEP functions have been explored. A key contribution of this work is the identification of a significant connection between weakly-strongly E-invex functions and SLUEP functions. As an application, we consider a nonlinear programming problem involving SLUEP functions. Under certain conditions, we prove that a local minimum of the problem is also a global minimum. Moreover, the sufficiency of Karush-Kuhn-Tucker (KKT) optimality conditions by considering the objective and constraint functions are SLUEI and SEI respectively. The theoretical results are validated through illustrative examples and counterexamples.

math.OC↗

arXiv2025

On the Characterization of gH-partial derivatives and gH-Product for Interval-Valued Functions

In this paper, we show by a counterexample that the gH-partial derivative of interval-valued functions (IVFs) may exist even when the partial derivative of the end point functions do not. Next, we introduce the gH-partial derivative in terms of gH-derivative and discuss its complete characterization. Furthermore, we introduce the gH-product of a vector with an n-tuples of intervals and illustrate by a suitable example that our definition refines the definition existing in the literature. To illustrate and validate these definitions, we provide several non-trivial examples.

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