Semi-$ (E, F) $-convexity in complex programming problems

M. E. Elbrolosy; M. E. Elbrolosy

doi:10.3934/math.2022621

AIMS Mathematics

2022, Volume 7, Issue 6: 11119-11131. doi: 10.3934/math.2022621

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Research article

Semi-$ (E, F) $-convexity in complex programming problems

M. E. Elbrolosy ^{1,2
,
,}

1.
Department of Mathematics and Statistics, College of Science, King Faisal University, P. O. Box 400, Al-Ahsa 31982, Saudi Arabia
2.
Department of Mathematics, Faculty of Science, Tanta University, Tanta 31527, Egypt

Received: 15 December 2021 Revised: 13 March 2022 Accepted: 29 March 2022 Published: 08 April 2022
MSC : 32C15, 90C25, 90C30, 90C46

Under recent circulars on the notions of convexity for real sets and functions like $ E $-convexity and $ (E, F) $-convexity, we expand the notions of $ (E, F) $ and semi-$ (E, F) $-convexity to include domains and functions in complex space. We examine their properties and interrelationships. As a consequence, we apply the associated results on a non-linear semi-$ (E, F) $-convex programming problem with cone-constraints in complex space. We discuss the existence and uniqueness of its optimal solution and establish the necessary and sufficient conditions for a feasible point to be an optimal solution to such a problem. The related results in real space can be deduced as special cases.
- complex programming,
- $ (E, F) $-convexity,
- semi-$ (E, F) $-convexity,
- optimal solution
Citation: M. E. Elbrolosy. Semi-$ (E, F) $-convexity in complex programming problems[J]. AIMS Mathematics, 2022, 7(6): 11119-11131. doi: 10.3934/math.2022621

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Abstract

Under recent circulars on the notions of convexity for real sets and functions like $ E $-convexity and $ (E, F) $-convexity, we expand the notions of $ (E, F) $ and semi-$ (E, F) $-convexity to include domains and functions in complex space. We examine their properties and interrelationships. As a consequence, we apply the associated results on a non-linear semi-$ (E, F) $-convex programming problem with cone-constraints in complex space. We discuss the existence and uniqueness of its optimal solution and establish the necessary and sufficient conditions for a feasible point to be an optimal solution to such a problem. The related results in real space can be deduced as special cases.

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