Proceedings of the
The Nineteenth International Conference on Computational Intelligence and Security (CIS 2023)
December 1 – 4, 2023, Haikou, China
Properties of $G-\alpha-E$--Semi-preinvex Functions and Applications in Nonlinear Programming
College of Mathematics and Computer Science, Yan'an University, China.
ABSTRACT
A new class of generalized convex functions, namely the G−α−E-semi-preinvex functions were proposed, which are a class of very important generalized convex functions. The real generalization of the α−E-semi-preinvex functions and the G−E−−semi-preinvex functions were also given. Firstly, some examples were given to prove the existence of G−α−E-semi-preinvex functions and the dependence on the relation of generalized convex functions. Then, some basic characteristics of the G−α−E-semi-preinvex functions were discussed. Finally, some applications of the G−α−E-semi-preinvex functions to unconstrained and inequation-constrained nonlinear programming problems were studied, and some optimality results were obtained; in addition, some examples were used to illustrate the correctness of the results obtained.
Keywords: α−E-semi-invariant convex set, G−α−E-semi-preinvex function, Basic characteristics, Nonlinear programming.
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College of Mathematics and Computer Science, Yan'an University, China.
ABSTRACT
A new class of generalized convex functions, namely the G−α−E-semi-preinvex functions were proposed, which are a class of very important generalized convex functions. The real generalization of the α−E-semi-preinvex functions and the G−E−−semi-preinvex functions were also given. Firstly, some examples were given to prove the existence of G−α−E-semi-preinvex functions and the dependence on the relation of generalized convex functions. Then, some basic characteristics of the G−α−E-semi-preinvex functions were discussed. Finally, some applications of the G−α−E-semi-preinvex functions to unconstrained and inequation-constrained nonlinear programming problems were studied, and some optimality results were obtained; in addition, some examples were used to illustrate the correctness of the results obtained.
Keywords: α−E-semi-invariant convex set, G−α−E-semi-preinvex function, Basic characteristics, Nonlinear programming.
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