Optimality for nonsmooth minimax fractional and multiobjective fractional optimization
Optimization Eruditorum, Volume 3, Issue 1, April 2026, Pages 7–19
JIAN HUANG
School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, Sichuan Province, China
LIGUO JIAO
Academy for Advanced Interdisciplinary Studies, Northeast Normal University, Changchun 130024, Jilin Province, China
DO SANG KIM
Department of Applied Mathematics, Pukyong National University, Busan 48513, Korea
Abstract
We establish optimality conditions for nonsmooth minimax fractional optimization problems with inequality and equality constraints in an Asplund space setting. Employing some advanced tools of variational analysis and generalized differentiation, we present necessary conditions for local optimal solutions under the constraint qualification. Sufficient conditions for the existence of global optimal solutions to the considered problem are also obtained by means of proposing the use of generalized convex-affine functions. In addition, some of these results are applied to multiobjective fractional optimization problems. Examples are given for analyzing and illustrating the obtained results.
Cite this Article as
Jian Huang, Liguo Jiao, Do Sang Kim, Waste collection problem: mathematical model and solution method, Optimization Eruditorum, 3(1), 7–19, 2026