scholarly journals Optimality Conditions and Duality of Three Kinds of Nonlinear Fractional Programming Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Xiaomin Zhang ◽  
Zezhong Wu
Keyword(s):  
Optimality Conditions ◽  
Convex Functions ◽  
Fractional Programming ◽  
Objective Functions ◽  
Duality Results ◽  
Nonlinear Fractional Programming

Some assumptions for the objective functions and constraint functions are given under the conditions of convex and generalized convex, which are based on theF-convex,ρ-convex, and(F,ρ)-convex. The sufficiency of Kuhn-Tucker optimality conditions and appropriate duality results are proved involving(F,ρ)-convex,(F,α,ρ,d)-convex, and generalized(F,α,ρ,d)-convex functions.

scholarly journals Optimality and duality in continuous-time nonlinear fractional programming

1992 ◽  
Vol 34 (2) ◽  
pp. 229-244 ◽  
Author(s):  
S. Suneja ◽  
C. Singh ◽  
R. N. Kaul
Keyword(s):  
Optimality Conditions ◽  
Programming Problem ◽  
Continuous Time ◽  
Fractional Programming ◽  
Dual Problem ◽  
Fractional Programming Problem ◽  
Duality Results ◽  
Perturbation Functions ◽  
Optimality And Duality ◽  
Nonlinear Fractional Programming

AbstractOptimality conditions via subdifferentiability and generalised Charnes-Cooper transformation are obtained for a continuous-time nonlinear fractional programming problem. Perturbation functions play a key role in the development. A dual problem is presented and certain duality results are obtained.

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 Duality for multiobjective fractional programming problems involving d -type-I n-set functions

2009 ◽  
Vol 19 (1) ◽  
pp. 63-73
Author(s):  
I.M. Stancu-Minasian ◽  
Gheorghe Dogaru ◽  
Mădălina Stancu
Keyword(s):  
Programming Problem ◽  
Fractional Programming ◽  
Generalized Convexity ◽  
Type I ◽  
Multiobjective Fractional Programming ◽  
Fractional Programming Problem ◽  
Duality Results ◽  
Set Functions ◽  
Convexity Assumptions ◽  
Nonlinear Fractional Programming

We establish duality results under generalized convexity assumptions for a multiobjective nonlinear fractional programming problem involving d -type-I n -set functions. Our results generalize the results obtained by Preda and Stancu-Minasian [24], [25].

scholarly journals Sufficiency and duality of set-valued fractional programming problems via second-order contingent epiderivative

2021 ◽  
pp. 19-19
Author(s):  
Koushik Das
Keyword(s):  
Optimality Conditions ◽  
Programming Problem ◽  
Fractional Programming ◽  
Second Order ◽  
Primal Problem ◽  
Duality Results ◽  
Contingent Epiderivative ◽  
Convexity Assumptions ◽  
Mixed Types ◽  
Cone Convexity

In this paper, we establish second-order sufficient KKT optimality conditions of a set-valued fractional programming problem under second-order generalized cone convexity assumptions. We also prove duality results between the primal problem and second-order dual problems of parametric, Mond-Weir, Wolfe, and mixed types via the notion of second-order contingent epiderivative.

scholarly journals Optimality and duality results for E-differentiable multiobjective fractional programming problems under E-convexity

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Tadeusz Antczak ◽  
Najeeb Abdulaleem
Keyword(s):  
Optimality Conditions ◽  
Fractional Programming ◽  
Optimization Problems ◽  
Necessary Optimality Conditions ◽  
Multiobjective Fractional Programming ◽  
New Class ◽  
Duality Results ◽  
Nonsmooth Vector Optimization ◽  
Differentiable Functions ◽  
Optimality And Duality

Abstract A new class of (not necessarily differentiable) multiobjective fractional programming problems with E-differentiable functions is considered. The so-called parametric E-Karush–Kuhn–Tucker necessary optimality conditions and, under E-convexity hypotheses, sufficient E-optimality conditions are established for such nonsmooth vector optimization problems. Further, various duality models are formulated for the considered E-differentiable multiobjective fractional programming problems and several E-duality results are derived also under appropriate E-convexity hypotheses.

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