scholarly journals Optimality conditions via scalarization for approximate quasi efficiency in multiobjective optimization

Filomat ◽  
2017 ◽  
Vol 31 (3) ◽  
pp. 671-680 ◽  
Author(s):  
Mehrdad Ghaznavi
Keyword(s):  
Multiobjective Optimization ◽  
Optimality Conditions ◽  
Optimization Problem ◽  
Original Problem ◽  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Multiobjective Optimization Problem ◽  
Alternative Theorem ◽  
Convexity Assumptions ◽  
Interesting Area

Approximate problems that scalarize and approximate a given multiobjective optimization problem (MOP) became an important and interesting area of research, given that, in general, are simpler and have weaker existence requirements than the original problem. Recently, necessary conditions for approximation of several types of efficiency for MOPs have been obtained through the use of an alternative theorem. In this paper, we use these results in order to extend them to sufficient conditions for approximate quasi (weak, proper) efficiency. For this, we use two scalarization techniques of Tchebycheff type. All the provided results are established without convexity assumptions.

scholarly journals Optimality Conditions for a Nonsmooth Uncertain Multiobjective Programming Problem

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Wenyan Han ◽  
Guolin Yu ◽  
Tiantian Gong
Keyword(s):  
Optimality Conditions ◽  
Generalized Convexity ◽  
Multiobjective Programming ◽  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Efficient Solutions ◽  
Type I ◽  
Generalized Convex Functions ◽  
Alternative Theorem ◽  
Multiobjective Programming Problem

This note is devoted to the investigation of optimality conditions for robust approximate quasi weak efficient solutions to a nonsmooth uncertain multiobjective programming problem (NUMP). Firstly, under the extended nonsmooth Mangasarian–Fromovitz constrained qualification assumption, the optimality necessary conditions of robust approximate quasi weak efficient solutions are given by using an alternative theorem. Secondly, a class of generalized convex functions is introduced to the problem (NUMP), which is called the pseudoquasi-type-I function, and its existence is illustrated by a concrete example. Finally, under the pseudopseudo-type-I generalized convexity hypothesis, the optimality sufficient conditions for robust approximate quasi weak efficient solutions to the problem (NUMP) are established.

scholarly journals Necessary optimality conditions for a fractional multiobjective optimization problem

2020 ◽  
Author(s):  
Nazih Abderrazzak Gadhi ◽  
khadija hamdaoui ◽  
mohammed El idrissi ◽  
Fatima zahra Rahou
Keyword(s):  
Multiobjective Optimization ◽  
Optimality Conditions ◽  
Optimization Problem ◽  
Constraint Qualification ◽  
Optimization Problems ◽  
Necessary Optimality Conditions ◽  
Multiobjective Optimization Problem ◽  
Support Functions

In this paper, we are concerned with a fractional multiobjective optimization problem (P). Using support functions together with a generalized Guignard constraint qualification, we give necessary optimality conditions in terms of convexificators and the Karush-Kuhn-Tucker multipliers. Several intermediate optimization problems have been introduced to help us in our investigation.

scholarly journals Sufficient optimality conditions and Mond-Weir duality results for a fractional multiobjective optimization problem

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Nazih Abderrazzak Gadhi ◽  
Fatima Zahra Rahou
Keyword(s):  
Multiobjective Optimization ◽  
Optimality Conditions ◽  
Optimization Problem ◽  
Necessary Optimality Conditions ◽  
Sufficient Optimality Conditions ◽  
Multiobjective Optimization Problem ◽  
Support Functions ◽  
Duality Results ◽  
The Given ◽  
Generalized Convexities

<p style='text-indent:20px;'>In this work, we are concerned with a fractional multiobjective optimization problem <inline-formula><tex-math id="M1">\begin{document}$ (P) $\end{document}</tex-math></inline-formula> involving set-valued maps. Based on necessary optimality conditions given by Gadhi et al. [<xref ref-type="bibr" rid="b14">14</xref>], using support functions, we derive sufficient optimality conditions for <inline-formula><tex-math id="M2">\begin{document}$ \left( P\right) , $\end{document}</tex-math></inline-formula> and we establish various duality results by associating the given problem with its Mond-Weir dual problem <inline-formula><tex-math id="M3">\begin{document}$ \left( D\right) . $\end{document}</tex-math></inline-formula> The main tools we exploit are convexificators and generalized convexities. Examples that illustrates our findings are also given.</p>

scholarly journals Constraint qualifications in nonsmooth multiobjective optimization problem

Filomat ◽  
2017 ◽  
Vol 31 (3) ◽  
pp. 781-797 ◽  
Author(s):  
Rekha Gupta ◽  
Manjari Srivastava
Keyword(s):  
Multiobjective Optimization ◽  
Optimality Conditions ◽  
Optimization Problem ◽  
Constraint Qualifications ◽  
Necessary Optimality Conditions ◽  
Inequality Constraint ◽  
Efficient Solutions ◽  
Equality Constraints ◽  
Regularity Conditions ◽  
Multiobjective Optimization Problem

A multiobjective optimization problem (MOP) with inequality and equality constraints is considered where the objective and inequality constraint functions are locally Lipschitz and equality constraint functions are differentiable. Burachik and Rizvi [J. Optim. Theory Appl. 155, 477-491 (2012)] gave Guignard and generalized Abadie regularity conditions for a differentiable programming problem and derived Karush-Kuhn-Tucker (KKT) type necessary optimality conditions. In this paper, we have defined the nonsmooth versions of Guignard and generalized Abadie regularity conditions given by Burachik and Rizvi and obtained KKT necessary optimality conditions for efficient and weak efficient solutions of (MOP). Further several constraint qualifications sufficient for the above newly defined constraint qualifications are introduced for (MOP) with no equality constraints. Relationships between them are presented and examples are constructed to support the results.

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