Papers by Najeeb Abdulaleem ( Najeeb Abbas Ahmed Abdulaleem Al-Sharabi )
Duality results for E-differentiable V-E-invex vector optimization problems
In this paper, a class of E-differentiable V-E-invex vector optimization problems with both inequ... more In this paper, a class of E-differentiable V-E-invex vector optimization problems with both inequality and equality constraints is considered. For the considered E-differentiable vector optimization problems, the so-called vector Wolfe E-duality problem is defined and several Wolfe E-duality theorems are established under V-E-invexity hypotheses.
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In this paper, we introduce a new concept of sets and a new class of functions called $$\alpha$$ ... more In this paper, we introduce a new concept of sets and a new class of functions called $$\alpha$$ α -E-invex sets and V-E-preinvex functions. Furthermore, a new concept of generalized convexity is introduced for (not necessarily) differentiable vector optimization problems. Namely, the concept of V-E-type I functions is defined for E-differentiable vector optimization problem. A number of sufficiency results are established under various types of (generalized) V-E-type I requirements. Moreover, several E-duality theorems in the sense of Mond–Weir are proved under appropriate (generalized) V-E-type I functions.
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This paper is devoted to introduce and investigate a new exact penalty function method which is c... more This paper is devoted to introduce and investigate a new exact penalty function method which is called the $$l_{1}$$ l 1 exact penalty E-function method. Namely, we use the aforesaid exact penalty function method to solve a completely new class of nonconvex (not necessarily) differentiable mathematical programming problems, that is, E-differentiable minimization problems. Then, we analyze the most important from a practical point of view property of all exact penalty function methods, that is, exactness of the penalization. Thus, under appropriate E-convexity hypotheses, we prove the equivalence between the original E-differentiable extremum problem and its corresponding penalized optimization problem created in the introduced $$l_{1}$$ l 1 exact penalty E-function method. Further, we also present and investigate the algorithm for this exact penalty function method which minimizes the $$l_{1}$$ l 1 exact penalty E-function. The convergence theorem for the aforesaid algorithm is also...
Optimality conditions in a class of generalized convex optimization problems with the multiple interval-valued objective function
Systems and Soft Computing
Optimality conditions for a class of E-differentiable vector optimization problems with interval-valued objective functions under E-invexity
International Journal of Computer Mathematics
E-differentiable minimax programming under E-convexity
Annals of Operations Research
Results in Mathematics
In this paper, we introduce a new concept of sets and a new class of functions called E-univex se... more In this paper, we introduce a new concept of sets and a new class of functions called E-univex sets and E-univex functions, respectively. For an E-differentiable function, the concept of E-univexity is introduced by generalizing several concepts of generalized convexity earlier defined into optimization theory. In addition, some properties of E-differentiable E-univex functions are investigated. Further, also concepts of E-differentiable generalized E-univexity are introduced. Then, the sufficiency of the so-called E-Karush–Kuhn–Tucker necessary optimality conditions are proved for an E-differentiable nonlinear optimization problem in which the involved functions are E-univex and/or generalized E-univex.
Operations Research Forum
In this paper, a class of E-differentiable vector optimization problems with both inequality and ... more In this paper, a class of E-differentiable vector optimization problems with both inequality and equality constraints is considered. The so-called vector mixed E-dual problem is defined for the considered E-differentiable vector optimization problem with both inequality and equality constraints. Then, several mixed E-duality theorems are established under (generalized) V-E-invexity hypotheses.
E-duality results for E-differentiable vector optimization problems involving E-type I functions
Journal of Statistics and Management Systems, 2021
Abstract In this paper, the class of E-differentiable vector optimization problems is considered.... more Abstract In this paper, the class of E-differentiable vector optimization problems is considered. The so-called vector Wolfe and mixed E-duality problems are defined for the considered E-differentiable multiobjective programming problem and several Wolfe and mixed E-duality theorems are derived under appropriate E-type I functions.
In this paper, the class of E-differentiable vector optimization problems with both inequality an... more In this paper, the class of E-differentiable vector optimization problems with both inequality and equality constraints is considered. For such (not necessarily) differentiable vector optimization problems, The so-called scalar and vector Wolfe E-dual problems are defined for the considered E-differentiable multiobjective programming problem with both inequality and equality constraints and several E-dual theorems are established also under (generalized) E-invexity hypotheses. Key–Words: E-invex set, E-invex function, E-differentiable function, Wolfe E-duality.
KT-E-invexity in E-differentiable vector optimization problems
Journal of Physics: Conference Series, 2021
In this paper, a new concept of generalized convexity is introduced for E-differentiable vector o... more In this paper, a new concept of generalized convexity is introduced for E-differentiable vector optimization problems. Namely, the concept of KT-E-invexity is defined for (not necessarily) differentiable vector optimization problems in which the functions involved are E-differentiable. The sufficiency of the so-called E-Karush-Kuhn-Tucker optimality conditions is established for the considered E-differentiable multiobjective programming problem under assumption that is KT-E-invex at an E-Karush-Kuhn-Tucker point. Further, the examples of KT-E-invex optimization problems with E-differentiable functions are constructed to illustrate the aforesaid results. Moreover, the so-called vector Mond-Weir E-dual problem is also derived for the considered E-differentiable vector optimization problem and several E-duality theorems in the sense of Mond-Weir are derived under KT-E-invexity hypotheses. 2020 Mathematics Subject Classification: 90C26, 90C29, 90C30, 90C46.
In this paper, a class of E-differentiable multiobjective programming problems with both inequali... more In this paper, a class of E-differentiable multiobjective programming problems with both inequality and equality constraints is considered. The so-called E-Karush-Kuhn-Tucker necessary optimality conditions are established for such nonsmooth vector optimization problems. Also, the sufficiency of these necessary optimality conditions are proved for E-differentiable multiobjective programming problems under (generalized) E-invexity hypotheses. Key–Words: E-differentiable vector optimization problem; E-optimality conditions; E-invex set; E-invex function with respect to η.
Wolfe E-duality for E-differentiable E-invex Vector Optimization Problems with Inequality and Equality Constraints
2018 International Conference on Applied Mathematics & Computational Science (ICAMCS.NET), 2018
In this paper, the class of E-differentiable vector optimization problems with both inequality an... more In this paper, the class of E-differentiable vector optimization problems with both inequality and equality constraints is considered. For such (not necessarily) differentiable vector optimization problems, The so-called scalar and vector Wolfe E-dual problems are defined for the considered E-differentiable multiobjective programming problem with both inequality and equality constraints and several E-dual theorems are established also under (generalized) E-invexity hypotheses.
E-B-invexity in E-differentiable mathematical programming
Results in Control and Optimization, 2021
Journal of Inequalities and Applications, 2019
A new class of (not necessarily differentiable) multiobjective fractional programming problems wi... more A new class of (not necessarily differentiable) multiobjective fractional programming problems with E-differentiable functions is considered. The so-called parametric E-Karush–Kuhn–Tucker necessary optimality conditions and, under E-convexity hypotheses, sufficient E-optimality conditions are established for such nonsmooth vector optimization problems. Further, various duality models are formulated for the considered E-differentiable multiobjective fractional programming problems and several E-duality results are derived also under appropriate E-convexity hypotheses.
Journal of Physics: Conference Series, 2019
In this paper, a class of E-differentiable multiobjective programming problems with both inequali... more In this paper, a class of E-differentiable multiobjective programming problems with both inequality and equality constraints is considered. The so-called vector Mond-Weir E-dual problem and vector mixed E-duality problem are defined for the considered E-differentiable multiobjective programming problem with both inequality and equality constraints and several Mond-Weir and mixed E-duality theorems are established under (generalized) E-invexity hypotheses.
Journal of Mathematics and Statistics, 2019
In this study, the class of E-differentiable vector optimization problems with both inequality an... more In this study, the class of E-differentiable vector optimization problems with both inequality and equality constraints is considered. For such (not necessarily) differentiable multicriteria optimization problems, two E-Lagrange functions and their -ܧsaddle points are defined. Then the so-called -ܧsaddle point criteria are established for such (not necessarily) differentiable multiobjective programming problems with Edifferentiable -ܧconvex functions.
Journal of Industrial & Management Optimization, 2017
In this paper, a nonconvex vector optimization problem with multiple interval-valued objective fu... more In this paper, a nonconvex vector optimization problem with multiple interval-valued objective function and both inequality and equality constraints is considered. The functions constituting it are not necessarily differentiable, but they are E-differentiable. The so-called E-Karush-Kuhn-Tucker necessary optimality conditions are established for the considered E-differentiable vector optimization problem with the multiple interval-valued objective function. Also the sufficient optimality conditions are derived for such intervalvalued vector optimization problems under appropriate (generalized) E-convexity hypotheses.
Journal of Nonlinear Sciences and Applications, 2019
In this paper, a nonconvex vector optimization problem with both inequality and equality constrai... more In this paper, a nonconvex vector optimization problem with both inequality and equality constraints is considered. The functions constituting it are not necessarily differentiable, but they are E-differentiable. The so-called E-Fritz John necessary optimality conditions and the so-called E-Karush-Kuhn-Tucker necessary optimality conditions are established for the considered E-differentiable multiobjective programming problems with both inequality and equality constraints. Further, the sufficient optimality conditions are derived for such nonconvex nonsmooth vector optimization problems under (generalized) E-convexity. The so-called vector E-Wolfe dual problem is defined for the considered E-differentiable multiobjective programming problem with both inequality and equality constraints and several dual theorems are established also under (generalized) E-convexity hypotheses.
ITM Web of Conferences, 2019
In this paper, a new concept of generalized convexity is introduced for not necessarily differenti... more In this paper, a new concept of generalized convexity is introduced for not necessarily differentiable vector optimization problems. For an E-differentiable function, the concept of E-invexity is introduced as a generalization of the E-differentiable E-convexity notion. In addition, some properties of E-differentiable E-invex functions are investigated. Furthermore, the so-called E-Karush-Kuhn-Tucker necessary optimality conditions are established for the considered E-differentiable vector optimization problems with both inequality and equality constraints. Also, the sufficiency of the E-Karush-Kuhn-Tucker necessary optimality conditions are proved for such E-differentiable vector optimization problems in which the involved functions are E-invex and/or generalized E-invex.
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Papers by Najeeb Abdulaleem ( Najeeb Abbas Ahmed Abdulaleem Al-Sharabi )