Higher-order Mond-Weir converse duality in multiobjective programming involving cones

2013 ◽  
Vol 56 (11) ◽  
pp. 2389-2392 ◽  
Author(s):  
XinMin Yang ◽  
Jin Yang ◽  
Tsz Leung Yip ◽  
Kok Lay Teo
Keyword(s):  
Multiobjective Programming ◽  
Higher Order ◽  
Converse Duality

scholarly journals Multiobjective duality with ρ−(η,θ)-invexity

2005 ◽  
Vol 2005 (2) ◽  
pp. 175-180 ◽  
Author(s):  
C. Nahak ◽  
S. Nanda
Keyword(s):  
Programming Problem ◽  
Multiobjective Programming ◽  
Efficient Solutions ◽  
Duality Theorems ◽  
Converse Duality ◽  
Dual Problems ◽  
Properly Efficient Solutions ◽  
Multiobjective Programming Problem ◽  
Primal And Dual Problems ◽  
Primal And Dual

Under ρ−(η,θ)-invexity assumptions on the functions involved, weak, strong, and converse duality theorems are proved to relate properly efficient solutions of the primal and dual problems for a multiobjective programming problem.

scholarly journals Mixed Type Nondifferentiable Higher-Order Symmetric Duality over Cones

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 274 ◽  
Author(s):  
Izhar Ahmad ◽  
Khushboo Verma ◽  
Suliman Al-Homidan
Keyword(s):  
Mixed Type ◽  
Higher Order ◽  
Dual Model ◽  
Duality Theorems ◽  
Symmetric Duality ◽  
Converse Duality ◽  
Self Duality ◽  
Pseudoconvex Functions

A new mixed type nondifferentiable higher-order symmetric dual programs over cones is formulated. As of now, in the literature, either Wolfe-type or Mond–Weir-type nondifferentiable symmetric duals have been studied. However, we present a unified dual model and discuss weak, strong, and converse duality theorems for such programs under higher-order F - convexity/higher-order F - pseudoconvexity. Self-duality is also discussed. Our dual programs and results generalize some dual formulations and results appeared in the literature. Two non-trivial examples are given to show the uniqueness of higher-order F - convex/higher-order F - pseudoconvex functions and existence of higher-order symmetric dual programs.

scholarly journals Higher-Order Generalized Invexity in Control Problems

2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
S. K. Padhan ◽  
C. Nahak
Keyword(s):  
Control Problem ◽  
Strong Duality ◽  
Higher Order ◽  
Control Problems ◽  
Weak Duality ◽  
Converse Duality ◽  
Generalized Invexity ◽  
Duality Results ◽  
Higher Order Duality

We introduce a higher-order duality (Mangasarian type and Mond-Weir type) for the control problem. Under the higher-order generalized invexity assumptions on the functions that compose the primal problems, higher-order duality results (weak duality, strong duality, and converse duality) are derived for these pair of problems. Also, we establish few examples in support of our investigation.

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.

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