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.

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 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 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 Exact Penalization and Necessary Optimality Conditions for Multiobjective Optimization Problems with Equilibrium Constraints

2014 ◽  
Vol 2014 ◽  
pp. 1-13
Author(s):  
Shengkun Zhu ◽  
Shengjie Li
Keyword(s):  
Multiobjective Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Necessary Optimality Conditions ◽  
Inequality Constraints ◽  
Multiobjective Optimization Problem ◽  
Equilibrium Constraints ◽  
Exact Penalization ◽  
Multiobjective Optimization Problems ◽  
Weak Vector

A calmness condition for a general multiobjective optimization problem with equilibrium constraints is proposed. Some exact penalization properties for two classes of multiobjective penalty problems are established and shown to be equivalent to the calmness condition. Subsequently, a Mordukhovich stationary necessary optimality condition based on the exact penalization results is obtained. Moreover, some applications to a multiobjective optimization problem with complementarity constraints and a multiobjective optimization problem with weak vector variational inequality constraints are given.

scholarly journals Nonemptiness and Compactness of Solutions Set for Nondifferentiable Multiobjective Optimization Problems

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
Xin-kun Wu ◽  
Jia-wei Chen ◽  
Yun-zhi Zou
Keyword(s):  
Fixed Point ◽  
Multiobjective Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Efficient Solutions ◽  
Multiobjective Optimization Problem ◽  
Weakly Efficient Solutions ◽  
Set Constraints ◽  
Multiobjective Optimization Problems ◽  
Problems And Solutions

A nondifferentiable multiobjective optimization problem with nonempty set constraints is considered, and the equivalence of weakly efficient solutions, the critical points for the nondifferentiable multiobjective optimization problems, and solutions for vector variational-like inequalities is established under some suitable conditions. Nonemptiness and compactness of the solutions set for the nondifferentiable multiobjective optimization problems are proved by using the FKKM theorem and a fixed-point theorem.

Strong Karush–Kuhn–Tucker optimality conditions for multiobjective semi-infinite programming via tangential subdifferential

2018 ◽  
Vol 52 (4-5) ◽  
pp. 1019-1041 ◽  
Author(s):  
Le Thanh Tung
Keyword(s):  
Optimality Conditions ◽  
Necessary Optimality Conditions ◽  
Efficient Solutions ◽  
Regularity Conditions ◽  
Infinite Programming ◽  
Kkt Optimality Conditions ◽  
Theoretical Results

The main aim of this paper is to study strong Karush–Kuhn–Tucker (KKT) optimality conditions for nonsmooth multiobjective semi-infinite programming (MSIP) problems. By using tangential subdifferential and suitable regularity conditions, we establish some strong necessary optimality conditions for some types of efficient solutions of nonsmooth MSIP problems. In addition to the theoretical results, some examples are provided to illustrate the advantages of our outcomes.

scholarly journals Optimality conditions for robust weak sharp efficient solutions of nonsmooth uncertain multiobjective optimization problems

2021 ◽  
Author(s):  
Jutamas Kerdkaew ◽  
Rabian Wangkeeree ◽  
Rattanaporn Wangkeereee
Keyword(s):  
Multiobjective Optimization ◽  
Optimality Conditions ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Efficient Solutions ◽  
Sufficient Optimality Conditions ◽  
Nonconvex Functions ◽  
Multiobjective Optimization Problems ◽  
Necessary And Sufficient ◽  
Weak Sharp

AbstractIn this paper, we investigate an uncertain multiobjective optimization problem involving nonsmooth and nonconvex functions. The notion of a (local/global) robust weak sharp efficient solution is introduced. Then, we establish necessary and sufficient optimality conditions for local and/or the robust weak sharp efficient solutions of the considered problem. These optimality conditions are presented in terms of multipliers and Mordukhovich/limiting subdifferentials of the related functions.

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