scholarly journals Optimality Conditions and Duality for Multiobjective Variational Problems with Generalized -B-Type-I Functions

2011 ◽  
Vol 2011 ◽  
pp. 1-11 ◽  
Author(s):  
C. Nahak ◽  
N. Behera
Keyword(s):  
Optimality Conditions ◽  
Variational Problems ◽  
Sufficient Optimality Conditions ◽  
Type I ◽  
Duality Results ◽  
Multiobjective Variational Problems ◽  
Generalized Type

We use -type-I and generalized -type-I functions to establish sufficient optimality conditions and duality results for multiobjective variational problems. Some of the related problems are also discussed.

scholarly journals Optimality condition and duality in multi objective programming with generalized (φ,ρ)-univexity

1970 ◽  
Vol 7 (1) ◽  
pp. 105-112
Author(s):  
Deo Brat Ojha
Keyword(s):  
Efficient Solution ◽  
Optimization Problem ◽  
Feasible Solution ◽  
Sufficient Optimality Conditions ◽  
Type I ◽  
Duality Results ◽  
Multi Objective Programming ◽  
Vector Valued Functions ◽  
Vector Valued ◽  
Generalized Type

In this paper, we extend the classes of generalized type I vector valued functions introduced by Aghezzaf and Hachimi[1] to generalized univex type I vector-valued functions and consider a multiobjective optimization problem involving generalized type I function with (φ,r ) -univexity. A number of Kuhn-Tucker type sufficient optimality conditions are obtained for a feasible solution to be an efficient solution. The Mond-Weir and general Mond-Weir type duality results are also presented. DOI: http://dx.doi.org/ 10.3126/kuset.v7i1.5427 KUSET 2011; 7(1): 105-112

scholarly journals Nonsmooth Vector Optimization Problem Involving Second-Order Semipseudo, Semiquasi Cone-Convex Functions

2020 ◽  
Vol 9 (2) ◽  
pp. 383-398
Author(s):  
Sunila Sharma ◽  
Priyanka Yadav
Keyword(s):  
Optimality Conditions ◽  
Vector Optimization ◽  
Convex Functions ◽  
Optimization Problem ◽  
Vector Optimization Problem ◽  
Second Order ◽  
Sufficient Optimality Conditions ◽  
Duality Results ◽  
Nonsmooth Vector Optimization ◽  
Second Order Cone

Recently, Suneja et al. [26] introduced new classes of second-order cone-(η; ξ)-convex functions along with theirgeneralizations and used them to prove second-order Karush–Kuhn–Tucker (KKT) type optimality conditions and duality results for the vector optimization problem involving first-order differentiable and second-order directionally differentiable functions. In this paper, we move one step ahead and study a nonsmooth vector optimization problem wherein the functions involved are first and second-order directionally differentiable. We introduce new classes of nonsmooth second-order cone-semipseudoconvex and nonsmooth second-order cone-semiquasiconvex functions in terms of second-order directional derivatives. Second-order KKT type sufficient optimality conditions and duality results for the same problem are proved using these functions.

scholarly journals Optimality and duality for a class of nondifferentiable minimax fractional programming problems

2009 ◽  
Vol 19 (1) ◽  
pp. 49-61
Author(s):  
Antoan Bătătorescu ◽  
Miruna Beldiman ◽  
Iulian Antonescu ◽  
Roxana Ciumara
Keyword(s):  
Optimality Conditions ◽  
Fractional Programming ◽  
Dual Problem ◽  
Sufficient Optimality Conditions ◽  
Square Root ◽  
Duality Results ◽  
Minimax Fractional Programming ◽  
Optimality And Duality ◽  
Necessary And Sufficient

Necessary and sufficient optimality conditions are established for a class of nondifferentiable minimax fractional programming problems with square root terms. Subsequently, we apply the optimality conditions to formulate a parametric dual problem and we prove some duality results.

CONE CONVEX AND RELATED FUNCTIONS IN OPTIMIZATION OVER TOPOLOGICAL VECTOR SPACES

2007 ◽  
Vol 24 (06) ◽  
pp. 741-754
Author(s):  
S. K. SUNEJA ◽  
MEETU BHATIA
Keyword(s):  
Optimality Conditions ◽  
Minimization Problem ◽  
Convex Functions ◽  
Strong Duality ◽  
Vector Spaces ◽  
Sufficient Optimality Conditions ◽  
Topological Vector Spaces ◽  
Duality Results ◽  
Gateaux Derivatives ◽  
Vector Valued

In this paper cone convex and related functions have been studied. The concept of cone semistrictly convex functions on topological vector spaces is introduced as a generalization of semistrictly convex functions. Certain properties of these functions have been established and their interrelations with cone convex and cone subconvex functions have been explored. Assuming the functions to be cone subconvex, sufficient optimality conditions are proved for a vector valued minimization problem over topological vector spaces, involving Gâteaux derivatives. A Mond-Weir type dual is associated and weak and strong duality results are proved.

scholarly journals Higher order optimality and duality in fractional vector optimization over cones

2017 ◽  
Vol 48 (3) ◽  
pp. 273-287 ◽  
Author(s):  
Muskan Kapoor ◽  
Surjeet Kaur Suneja ◽  
Meetu Bhatia Grover
Keyword(s):  
Optimality Conditions ◽  
Vector Optimization ◽  
Convex Functions ◽  
Optimization Problem ◽  
Vector Optimization Problem ◽  
Higher Order ◽  
Sufficient Optimality Conditions ◽  
Dual Program ◽  
Duality Results ◽  
Optimality And Duality

In this paper we give higher order sufficient optimality conditions for a fractional vector optimization problem over cones, using higher order cone-convex functions. A higher order Schaible type dual program is formulated over cones.Weak, strong and converse duality results are established by using the higher order cone convex and other related functions.

scholarly journals Optimality conditions and Mond–Weir duality for a class of differentiable semi-infinite multiobjective programming problems with vanishing constraints

4OR ◽  
2021 ◽  
Author(s):  
Tadeusz Antczak
Keyword(s):  
Optimality Conditions ◽  
Vector Optimization ◽  
Multiobjective Programming ◽  
Optimization Problems ◽  
Necessary Optimality Conditions ◽  
Sufficient Optimality Conditions ◽  
Smooth Vector ◽  
Duality Results ◽  
Vanishing Constraints ◽  
Multiobjective Programming Problems

AbstractIn this paper, the class of differentiable semi-infinite multiobjective programming problems with vanishing constraints is considered. Both Karush–Kuhn–Tucker necessary optimality conditions and, under appropriate invexity hypotheses, sufficient optimality conditions are proved for such nonconvex smooth vector optimization problems. Further, vector duals in the sense of Mond–Weir are defined for the considered differentiable semi-infinite multiobjective programming problems with vanishing constraints and several duality results are established also under invexity hypotheses.

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