scholarly journals Higher-order duality results for a new class of nonconvex nonsmooth multiobjective programming problems

Filomat ◽  
2019 ◽  
Vol 33 (6) ◽  
pp. 1619-1639
Author(s):  
Tadeusz Antczak ◽  
Hachem Slimani
Keyword(s):  
Multiobjective Programming ◽  
Vector Optimization Problem ◽  
Order Type ◽  
Higher Order ◽  
Type I ◽  
New Class ◽  
Duality Results ◽  
Nonsmooth Multiobjective Programming ◽  
Multiobjective Programming Problem ◽  
Multiobjective Programming Problems

In this paper, a nonconvex nonsmooth multiobjective programming problem is considered and two its higher-order duals are defined. Further, several duality results are established between the considered nonsmooth vector optimization problem and its dual models under assumptions that the involved functions are higher-order (??)-type I functions.

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 Generalized -Type I Univex Functions in Multiobjective Optimization

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Pallavi Kharbanda ◽  
Divya Agarwal ◽  
Deepa Sinha
Keyword(s):  
Multiobjective Programming ◽  
Generalized Functions ◽  
Sufficient Optimality Conditions ◽  
Type I ◽  
Duality Theorems ◽  
New Class ◽  
Nonsmooth Multiobjective Programming ◽  
Strong Converse ◽  
Multiobjective Programming Problem ◽  
Generalized Type

A new class of generalized functions -type I univex is introduced for a nonsmooth multiobjective programming problem. Based upon these generalized functions, sufficient optimality conditions are established. Weak, strong, converse, and strict converse duality theorems are also derived for Mond-Weir-type multiobjective dual program.

Higher order duality for cone vector optimization problems

2018 ◽  
Vol 13 (01) ◽  
pp. 2050020
Author(s):  
Vivek Singh ◽  
Anurag Jayswal ◽  
S. Al-Homidan ◽  
I. Ahmad
Keyword(s):  
Vector Optimization ◽  
Optimization Problems ◽  
Strong Duality ◽  
Vector Optimization Problem ◽  
Higher Order ◽  
Support Functions ◽  
Invex Functions ◽  
New Class ◽  
Duality Results ◽  
Higher Order Duality

In this paper, we present a new class of higher order [Formula: see text]-[Formula: see text]-invex functions over cones. Further, we formulate two types of higher order dual models for a vector optimization problem over cones containing support functions in objectives as well as in constraints and establish several duality results, viz., weak and strong duality results.

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.

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.

Multiobjective Programming

2014 ◽  
pp. 1585-1604
Author(s):  
Minghe Sun
Keyword(s):  
Programming Problem ◽  
Multiobjective Programming ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Objective Functions ◽  
Solution Quality ◽  
Solution Methods ◽  
Multiobjective Programming Problem ◽  
Feasible Solutions ◽  
Multiobjective Programming Problems

Optimization problems with multiple criteria measuring solution quality can be modeled as multiobjective programming problems. Because the objective functions are usually in conflict, there is not a single feasible solution that can optimize all objective functions simultaneously. An optimal solution is one that is most preferred by the decision maker (DM) among all feasible solutions. An optimal solution must be nondominated but a multiobjective programming problem may have, possibly infinitely, many nondominated solutions. Therefore, tradeoffs must be made in searching for an optimal solution. Hence, the DM's preference information is elicited and used when a multiobjective programming problem is solved. The model, concepts and definitions of multiobjective programming are presented and solution methods are briefly discussed. Examples are used to demonstrate the concepts and solution methods. Graphics are used in these examples to facilitate understanding.

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