Connections between Some Extremization Problems and Associated Inequalities-Reference-Cited by-同舟云学术

Connections between Some Extremization Problems and Associated Inequalities

Published:2024-09-11 Issue:9 Volume:13 Page:614
ISSN:2075-1680
Container-title:Axioms
language:en
Short-container-title:Axioms

Author:

Xu Wei¹,Treanţă Savin²³⁴^ORCID

Affiliation:

1. Computer Science Department, New York University, 251 Mercer Street, New York, NY 10012, USA

2. Faculty of Applied Sciences, National University of Science and Technology Politehnica Bucharest, 060042 Bucharest, Romania

3. Academy of Romanian Scientists, 54 Splaiul Independentei, 050094 Bucharest, Romania

4. Fundamental Sciences Applied in Engineering—Research Center, National University of Science and Technology Politehnica Bucharest, 060042 Bucharest, Romania

Abstract

In this paper, we investigate and characterize a family of optimization problems introduced by interval-valued functionals that are determined by curvilinear integrals. To this end, we first state the path independence and (strictly) LU convexity properties of the considered functionals. Thereafter, we formulate the corresponding controlled variational inequalities. The main results of this paper provide some connections for the above-mentioned variational models. Since the objective functionals have a physical importance, an illustrative application is considered and studied by using the theoretical elements obtained in this study.

Publisher

MDPI AG

Link

https://www.mdpi.com/2075-1680/13/9/614/pdf

Reference36 articles.

1. On some non-linear elliptic differential-functional equations;Hartman;Acta Math.,1966

2. Giannessi, F. (1980). Theorems of alternative, quadratic programs and complementarity problems. Variational Inequalities and Complementarity Problems (Proc. Internat. School, Erice, 1978), Wiley.

3. Moore, R.E. (1966). Interval Analysis, Prentice-Hall.

4. Moore, R.E. (1979). Methods and Applications of Interval Analysis, SIAM.

5. Generalized Hukuhara differentiability of interval-valued functions and interval differential equations;Stefanini;Nonlinear Anal.,2009