Fixed Point Methods and Optimization

Electronic ISSN: 3008-1548

DOI: 10.69829/fpmo

Generalized convex interval-valued functions and interval-valued optimization under total order relations

Fixed Point Methods and Optimization, Volume 2, Issue 1, April 2025, Pages 94–109

XIN-YUE TAN

College of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing 400074, China

ZAI-YUN PENG

College of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing 400074, China

SIMEON REICH

Department of Mathematics, The Technion– Israel Institute of Technology, 3200003 Haifa, Israel

YEKINI SHEHU

School of Mathematical Sciences, Zhejiang Normal University, Jinhua, 321004, China


Abstract

A class of CR-E-semi-preinvex interval-valued functions under the CR total order is proposed, and the optimality conditions of the interval-valued optimization problem are studied. Through theoretical derivation, the definition of the CR-E-semi-preinvex interval-valued function is obtained, and an example is given to verify the existence of the CR-E-semi-preinvex interval-valued function. The related properties of the CR-E-semi-preinvex interval-valued function and a class of CR-E-semi-preinvex interval-valued optimization problems are studied. The relationship between the CR-E-semi-preinvex interval-valued function and the CR-E-semi-invex interval-valued function is obtained, and the sufficient and necessary conditions are obtained for the KKT optimality of the CR-E-semi-preinvex interval-valued optimization problem in the case of real-valued inequality constraints. This research expands the generalized convexity of interval-valued functions under the total order relation, which enriches the research on generalized convexity and makes the application of interval-valued optimization problems more extensive.


Cite this Article as

Xin-Yue Tan, Zai-Yun Peng, Simeon Reich, and Yekini Shehu, Generalized convex interval-valued functions and interval-valued optimization under total order relations, Fixed Point Methods and Optimization, 2(1), 94–109, 2025