\(E\)-optimality conditions and Wolfe \(E\)-duality for \(E\)-differentiable vector optimization problems with inequality and equality constraints
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Authors
Tadeusz Antczak
- Faculty of Mathematics and Computer Science, University of Lodz, Banacha 22, 90--238 Lodz, Poland.
Najeeb Abdulaleem
- Department of Mathematics, Hadhramout University, P. O. BOX: (50511-50512), Al-Mahrah, Yemen.
Abstract
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.
Share and Cite
ISRP Style
Tadeusz Antczak, Najeeb Abdulaleem, \(E\)-optimality conditions and Wolfe \(E\)-duality for \(E\)-differentiable vector optimization problems with inequality and equality constraints, Journal of Nonlinear Sciences and Applications, 12 (2019), no. 11, 745--764
AMA Style
Antczak Tadeusz, Abdulaleem Najeeb, \(E\)-optimality conditions and Wolfe \(E\)-duality for \(E\)-differentiable vector optimization problems with inequality and equality constraints. J. Nonlinear Sci. Appl. (2019); 12(11):745--764
Chicago/Turabian Style
Antczak, Tadeusz, Abdulaleem, Najeeb. "\(E\)-optimality conditions and Wolfe \(E\)-duality for \(E\)-differentiable vector optimization problems with inequality and equality constraints." Journal of Nonlinear Sciences and Applications, 12, no. 11 (2019): 745--764
Keywords
- \(E\)-differentiable function
- \(E\)-Fritz John necessary optimality conditions
- \(E\)-Karush-Kuhn-Tucker necessary optimality conditions
- \(E\)-Wolfe duality
- \(E\)-convex function
MSC
- 90C26
- 90C29
- 90C30
- 90C46
- 90C47
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