On optimality conditions for multiobjective optimization problems in topological vector space

In this paper, we consider convex multiobjective optimization problems with equality and inequality constraints in real Banach space. We establish saddle point necessary and sufficient Pareto optimality conditions for considered problems under some constraint qualifications. These results are motivated by the symmetric results obtained in the recent article by Cobos Sánchez et al. in 2021 on Pareto optimality for multiobjective optimization problems of continuous linear operators. The discussions in this paper are also related to second order symmetric duality for nonlinear multiobjective mixed integer programs for arbitrary cones due to Mishra and Wang in 2005. Further, we establish Karush–Kuhn–Tucker optimality conditions using saddle point optimality conditions for the differentiable cases and present some examples to illustrate our results. The study in this article can also be seen and extended as symmetric results of necessary and sufficient optimality conditions for vector equilibrium problems on Hadamard manifolds by Ruiz-Garzón et al. in 2019.

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Strong complementary approximate Karush-Kuhn-Tucker conditions for multiobjective optimization problems

Yugoslav journal of operations research ◽

10.2298/yjor210315024m ◽

2021 ◽

pp. 24-24

Author(s):

Jitendra Maurya ◽

Shashi Mishra

Keyword(s):

Multiobjective Optimization ◽

Optimality Conditions ◽

Constraint Qualification ◽

Optimization Problems ◽

Constraint Qualifications ◽

Inequality Constraints ◽

Multiobjective Optimization Problems ◽

Sequential Optimality Conditions ◽

Equality And Inequality Constraints ◽

Optim Theory

In this paper, we establish strong complementary approximate Karush- Kuhn-Tucker (SCAKKT) sequential optimality conditions for multiobjective optimization problems with equality and inequality constraints without any constraint qualifications and introduce a weak constraint qualification which assures the equivalence between SCAKKT and the strong Karush-Kuhn-Tucker (J Optim Theory Appl 80 (3): 483{500, 1994) conditions for multiobjective optimization problems.

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

Arabian Journal of Mathematics ◽

10.1007/s40065-021-00346-w ◽

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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