Quasi Semi and Pseudo Semi (p,E)-Convexity in Non-Linear Optimization Programming

Authors

Revan I. Hazim
Saba N. Majeed Department of Mathematics , College of Education for Pure Science,Ibn Al –Haitham, University of Baghdad https://orcid.org/0000-0001-9831-9666

DOI:

https://doi.org/10.30526/36.1.2928

Keywords:

(p,E)-convex set, (p,E)-convex function, quasi semi (p,E)-convex function, pseudo semi (p,E)-convex function

Abstract

The class of quasi semi -convex functions and pseudo semi -convex functions are presented in this paper by combining the class of -convex functions with the class of quasi semi -convex functions and pseudo semi -convex functions, respectively. Various non-trivial examples are introduced to illustrate the new functions and show their relationships with -convex functions recently introduced in the literature. Different general properties and characteristics of this class of functions are established. In addition, some optimality properties of generalized non-linear optimization problems are discussed. In this generalized optimization problems, we used, as the objective function, quasi semi -convex (respectively, strictly quasi semi -convex functions and pseudo semi -convex functions), and the constraint set is -convex set.

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