Open AccessSecond-Order characterizations for set-valued equilibrium problems with variable ordering structures
Author(s) -
Shasha Hu,
Yi Xu,
Yuhan Zhang
Publication year - 2022
Publication title -
journal of industrial and management optimization
Language(s) - English
Resource type - Journals
eISSN - 1553-166X
pISSN - 1547-5816
DOI - 10.3934/jimo.2020164
Subject(s) - convexity , mathematics , tangent , tangent cone , constraint (computer aided design) , mathematical optimization , order (exchange) , set (abstract data type) , variable (mathematics) , nonlinear system , computer science , mathematical analysis , geometry , physics , finance , quantum mechanics , financial economics , economics , programming language
The concepts of weakly efficient solutions and globally efficient solutions are introduced for constrained set-valued equilibrium problems with variable ordering structures. By applying the second-order tangent epiderivative and a nonlinear functional, necessary optimality conditions for weakly efficient solutions and globally efficient solutions are established without any convexity assumption. Under the cone-convexity of the objective and constraint functions, sufficient optimality conditions are given. In addition, the tangent derivatives of objective and constraint functions are separated. Simultaneously, a unified necessary and sufficient optimality conditions for weakly efficient solutions is derived, and the same goes for globally efficient solutions. In particular, we give specific examples to illustrate the optimality conditions, respectively.