Second-order optimality conditions for efficiency in $$C^{1,1}$$-smooth quasiconvex multiobjective programming problem

2021 ◽  
Vol 40 (6) ◽  
Author(s):  
Tran Van Su ◽  
Dinh Dieu Hang
Keyword(s):  
Optimality Conditions ◽  
Programming Problem ◽  
Multiobjective Programming ◽  
Second Order ◽  
Second Order Optimality Conditions ◽  
Multiobjective Programming Problem

Symmetric duality results for second-order nondifferentiable multiobjective programming problem

2019 ◽  
Vol 53 (2) ◽  
pp. 539-558 ◽  
Author(s):  
Ramu Dubey ◽  
Vishnu Narayan Mishra
Keyword(s):  
Programming Problem ◽  
Duality Theorem ◽  
Multiobjective Programming ◽  
Second Order ◽  
Weak Duality ◽  
Symmetric Duality ◽  
Numerical Examples ◽  
Duality Results ◽  
Duality Relations ◽  
Multiobjective Programming Problem

In this article, we study the existence of Gf-bonvex/Gf -pseudo-bonvex functions and construct various nontrivial numerical examples for the existence of such type of functions. Furthermore, we formulate Mond-Weir type second-order nondifferentiable multiobjective programming problem and give a nontrivial concrete example which justify weak duality theorem present in the paper. Next, we prove appropriate duality relations under aforesaid assumptions.

scholarly journals Sufficiency and Duality in Nonsmooth Multiobjective Programming Problem under Generalized Univex Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Pallavi Kharbanda ◽  
Divya Agarwal ◽  
Deepa Sinha
Keyword(s):  
Optimality Conditions ◽  
Programming Problem ◽  
Multiobjective Programming ◽  
Generalized Functions ◽  
Sufficient Optimality Conditions ◽  
Type I ◽  
Duality Theorems ◽  
Nonsmooth Multiobjective Programming ◽  
Strong Converse ◽  
Multiobjective Programming Problem

We consider a nonsmooth multiobjective programming problem where the functions involved are nondifferentiable. The class of univex functions is generalized to a far wider class of (φ,α,ρ,σ)-dI-V-type I univex functions. Then, through various nontrivial examples, we illustrate that the class introduced is new and extends several known classes existing in the literature. Based upon these generalized functions, Karush-Kuhn-Tucker type sufficient optimality conditions are established. Further, we derive weak, strong, converse, and strict converse duality theorems for Mond-Weir type multiobjective dual program.

scholarly journals Duality for a class of nonsmooth multiobjective programming problems using convexificators

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 489-498 ◽  
Author(s):  
Anurag Jayswal ◽  
Krishna Kummari ◽  
Vivek Singh
Keyword(s):  
Optimality Conditions ◽  
Programming Problem ◽  
Multiobjective Programming ◽  
Optimization Problems ◽  
Duality Results ◽  
Nonsmooth Multiobjective Programming ◽  
Multiobjective Programming Problem ◽  
Multiobjective Programming Problems ◽  
Dual Models

As duality is an important and interesting feature of optimization problems, in this paper, we continue the effort of Long and Huang [X. J. Long, N. J. Huang, Optimality conditions for efficiency on nonsmooth multiobjective programming problems, Taiwanese J. Math., 18 (2014) 687-699] to discuss duality results of two types of dual models for a nonsmooth multiobjective programming problem using convexificators.

scholarly journals Multiobjective programming under nondifferentiable G-V-invexity

Filomat ◽  
2016 ◽  
Vol 30 (11) ◽  
pp. 2909-2923 ◽  
Author(s):  
Tadeusz Antczak
Keyword(s):  
Optimality Conditions ◽  
Programming Problem ◽  
Dual Problem ◽  
Multiobjective Programming ◽  
Necessary Optimality Conditions ◽  
Vector Optimization Problem ◽  
Alternative Theorem ◽  
Nonsmooth Multiobjective Programming ◽  
Locally Lipschitz ◽  
Multiobjective Programming Problem

In the paper, new Fritz John type necessary optimality conditions and new Karush-Kuhn-Tucker type necessary opimality conditions are established for the considered nondifferentiable multiobjective programming problem involving locally Lipschitz functions. Proofs of them avoid the alternative theorem usually applied in such a case. The sufficiency of the introduced Karush-Kuhn-Tucker type necessary optimality conditions are proved under assumptions that the functions constituting the considered nondifferentiable multiobjective programming problem are G-V-invex with respect to the same function ?. Further, the so-called nondifferentiable vector G-Mond-Weir dual problem is defined for the considered nonsmooth multiobjective programming problem. Under nondifferentiable G-V-invexity hypotheses, several duality results are established between the primal vector optimization problem and its G-dual problem in the sense of Mond-Weir.

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