Extensions of proper efficiency in complex space

Youness, Ebrahim A.; Elbrolosy, M. E.

doi:10.1002/mma.4715

Cited by 3 publications

(1 citation statement)

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“…The solutions were characterized by optimal solutions of a related scalar problem and the efficiency conditions were investigated. Recently, some concepts of proper efficiency were extended for vector optimization problems in [16]. For more details concerning this type of optimization problems, the attentive reader can refer additional works like [2,3,6,10,[12][13][14] in real space, and [8,9,11] in complex space.…”

Section: Introductionmentioning

confidence: 99%

Criteria of saddle points for the general form of vector optimization problem in complex space

Elbrolosy¹

2020

Filomat

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In this paper, the criteria of the saddle point type for a general form of complex multi-objective programming problems are derived where the objective function of the problem is considered full complex. The criteria with/without differentiability assumptions imposed in the involved functions are developed. It is shown that the efficient solutions can be characterized in terms of saddle points whether the functions are differentiable or not. The obtained theoretical results are generalizations of their real correspondents in literature and complete the results in complex space.

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Section: Introductionmentioning

confidence: 99%

Criteria of saddle points for the general form of vector optimization problem in complex space

Elbrolosy¹

2020

Filomat

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A flexible objective-constraint approach and a new algorithm for constructing the Pareto front of multiobjective optimization problems

Hoseinpoor,

Ghaznavi

2024

Acta Math Sci

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

Elbrolosy

2022

MATH

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<abstract><p>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.</p></abstract>

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Extensions of proper efficiency in complex space

Cited by 3 publications

References 15 publications

Criteria of saddle points for the general form of vector optimization problem in complex space

Criteria of saddle points for the general form of vector optimization problem in complex space

A flexible objective-constraint approach and a new algorithm for constructing the Pareto front of multiobjective optimization problems

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

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