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.

scholarly journals Optimality and Duality for Multiobjective Fractional Programming Involving Nonsmooth Generalized(ℱ,b,ϕ,ρ,θ)-Univex Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Jen-Chwan Liu ◽  
Chun-Yu Liu
Keyword(s):  
Optimality Conditions ◽  
Fractional Programming ◽  
Necessary Optimality Conditions ◽  
Sufficient Optimality Conditions ◽  
Dual Model ◽  
Multiobjective Fractional Programming ◽  
Duality Results ◽  
Optimality And Duality ◽  
Necessary And Sufficient

We establish properly efficient necessary and sufficient optimality conditions for multiobjective fractional programming involving nonsmooth generalized(ℱ,b,ϕ,ρ,θ)-univex functions. Utilizing the necessary optimality conditions, we formulate the parametric dual model and establish some duality results in the framework of generalized(ℱ,b,ϕ,ρ,θ)-univex functions.

scholarly journals Optimality and Duality for Nondifferentiable Minimax Fractional Programming with Generalized Convexity

2011 ◽  
Vol 2011 ◽  
pp. 1-19 ◽  
Author(s):  
Anurag Jayswal
Keyword(s):  
Fractional Programming ◽  
Generalized Convexity ◽  
Optimality Criteria ◽  
Sufficient Optimality Conditions ◽  
View Point ◽  
Generalized Convex Functions ◽  
Duality Results ◽  
Minimax Fractional Programming ◽  
Optimality And Duality ◽  
Dual Models

We establish several sufficient optimality conditions for a class of nondifferentiable minimax fractional programming problems from a view point of generalized convexity. Subsequently, these optimality criteria are utilized as a basis for constructing dual models, and certain duality results have been derived in the framework of generalized convex functions. Our results extend and unify some known results on minimax fractional programming problems.

scholarly journals Minimax fractional programming with nondiferentiable (G,β)-invexity

Filomat ◽  
2014 ◽  
Vol 28 (10) ◽  
pp. 2027-2035 ◽  
Author(s):  
Xiaoling Liu ◽  
Dehui Yuan
Keyword(s):  
Optimality Conditions ◽  
Programming Problem ◽  
Fractional Programming ◽  
Dual Problem ◽  
Necessary Optimality Conditions ◽  
Minimax Programming ◽  
Fractional Programming Problem ◽  
Duality Results ◽  
Locally Lipschitz ◽  
Minimax Fractional Programming

In this paper, we consider the minimax fractional programming Problem (FP) in which the functions are locally Lipschitz (G,?)-invex. With the help of a useful auxiliary minimax programming problem, we obtain not only G-sufficient but also G-necessary optimality conditions theorems for the Problem (FP). With G-necessary optimality conditions and (G,?)-invexity in the hand, we further construct dual Problem (D) for the primal one (FP) and prove duality results between Problems (FP) and (D). These results extend several known results to a wider class of programs.

scholarly journals Efficiency and duality in nonsmooth multiobjective fractional programming involving η-pseudolinear functions

2012 ◽  
Vol 22 (1) ◽  
pp. 3-18 ◽  
Author(s):  
S.K. Mishra ◽  
B.B. Upadhyay
Keyword(s):  
Fractional Programming ◽  
Dual Problem ◽  
Feasible Solution ◽  
Strong Duality ◽  
Sufficient Optimality Conditions ◽  
Boundedness Condition ◽  
Multiobjective Fractional Programming ◽  
Duality Results ◽  
Multiobjective Fractional Programming Problem ◽  
Necessary And Sufficient

In this paper, we shall establish necessary and sufficient optimality conditions for a feasible solution to be efficient for a nonsmooth multiobjective fractional programming problem involving ?-pseudolinear functions. Furthermore, we shall show equivalence between efficiency and proper efficiency under certain boundedness condition. We have also obtained weak and strong duality results for corresponding Mond-Weir subgradient type dual problem. These results extend some earlier results on efficiency and duality to multiobjective fractional programming problems involving ?-pseudolinear and pseudolinear 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 Sufficient Conditions and Duality Theorems for Nondifferentiable Minimax Fractional Programming

2011 ◽  
Vol 2011 ◽  
pp. 1-22
Author(s):  
Shun-Chin Ho
Keyword(s):  
Optimality Conditions ◽  
Fractional Programming ◽  
Sufficient Conditions ◽  
Sufficient Optimality Conditions ◽  
Duality Theorems ◽  
Invex Functions ◽  
Duality Results ◽  
Wolfe Duality ◽  
Minimax Fractional Programming

We consider nondifferentiable minimax fractional programming problems involving B-(p, r)-invex functions with respect to η and b. Sufficient optimality conditions and duality results for a class of nondifferentiable minimax fractional programming problems are obtained undr B-(p, r)-invexity assumption on objective and constraint functions. Parametric duality, Mond-Weir duality, and Wolfe duality problems may be formulated, and duality results are derived under B-(p, r)-invex functions.

scholarly journals Optimality and duality in set-valued optimization utilizing limit sets

2018 ◽  
Vol 16 (1) ◽  
pp. 1128-1139
Author(s):  
Xiangyu Kong ◽  
Yinfeng Zhang ◽  
GuoLin Yu
Keyword(s):  
Optimality Conditions ◽  
Duality Theory ◽  
Optimization Problem ◽  
Convex Set ◽  
Sufficient Optimality Conditions ◽  
Constraint Optimization ◽  
Limit Sets ◽  
Optimality And Duality ◽  
Wolfe Type Dual ◽  
Necessary And Sufficient

AbstractThis paper deals with optimality conditions and duality theory for vector optimization involving non-convex set-valued maps. Firstly, under the assumption of nearly cone-subconvexlike property for set-valued maps, the necessary and sufficient optimality conditions in terms of limit sets are derived for local weak minimizers of a set-valued constraint optimization problem. Then, applications to Mond-Weir type and Wolfe type dual problems are presented.

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 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.

scholarly journals Nondifferentiable generalized minimax fractional programming under (Ф,ρ)-invexity

2021 ◽  
pp. 18-18
Author(s):  
B.B. Upadhyay ◽  
T. Antczak ◽  
S.K. Mishra ◽  
K. Shukla
Keyword(s):  
Optimality Conditions ◽  
Programming Problem ◽  
Fractional Programming ◽  
Sufficient Optimality Conditions ◽  
Duality Theorems ◽  
Dual Problems ◽  
Fractional Programming Problem ◽  
Minimax Fractional Programming ◽  
Dual Models

In this paper, a class of nonconvex nondifferentiable generalized minimax fractional programming problems is considered. Sufficient optimality conditions for the considered nondifferentiable generalized minimax fractional programming problem are established under the concept of (?,?)-invexity. Further, two types of dual models are formulated and various duality theorems relating to the primal minimax fractional programming problem and dual problems are established. The results established in the paper generalize and extend several known results in the literature to a wider class of nondifferentiable minimax fractional programming problems. To the best of our knowledge, these results have not been established till now.

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