scholarly journals Some results on symmetric duality of mathematical fractional programming with generalized $F$-convexity complex spaces

2005 ◽  
Vol 36 (2) ◽  
pp. 159-165
Author(s):  
Deo Brat Ojha
Keyword(s):  
Fractional Programming ◽  
General Type ◽  
Strong Duality ◽  
Objective Functions ◽  
Symmetric Duality ◽  
Support Functions ◽  
Complex Spaces ◽  
Duality Results ◽  
Special Cases ◽  
Convexity Assumptions

In this present article we have given some mathematical fractional programming problems with their symmetric duals and have derived weak and strong duality results with respect to such programs. Moreover, we have also used most general type of convexity assumptions involved with the functions which are related to the programming problems. It is to be pointed out that the objective functions in such programs contain terms like support functions which in turn are able to give results on particular classes of programs involving quadratic terms. Our results in particular give as of special cases some eariler results symmetric duals given in the current literature. All discussion goes to complex spaces.

scholarly journals On second- order symmetric duality for a class of multiobjective fractional programming problem

2012 ◽  
Vol 43 (2) ◽  
pp. 267-279 ◽  
Author(s):  
Deo Brat Ojha
Keyword(s):  
Fractional Programming ◽  
Strong Duality ◽  
Second Order ◽  
Multiobjective Fractional Programming ◽  
Duality Theorems ◽  
Symmetric Duality ◽  
Multiobjective Fractional Programming Problem ◽  
Special Cases ◽  
Second Order Symmetric Duality ◽  
Dual Models

This article is concerned with a pair of second-order symmetric duals in the context of non-differentiable multiobjective fractional programming problems. We establish the weak and strong duality theorems for the new pair of dual models. Discussion on some special cases shows that results in this paper extend previous work in this area.

scholarly journals Higher-order symmetric duality in nondifferentiable multiobjective optimization over cones

Filomat ◽  
2019 ◽  
Vol 33 (3) ◽  
pp. 711-724
Author(s):  
N. Kailey ◽  
S Sonali
Keyword(s):  
Convex Set ◽  
Compact Convex ◽  
Higher Order ◽  
Objective Functions ◽  
Duality Theorems ◽  
Symmetric Duality ◽  
Self Duality ◽  
Special Cases ◽  
Compact Convex Set ◽  
Convexity Assumptions

In this paper, a new pair of higher-order nondifferentiable multiobjective symmetric dual programs over arbitrary cones is formulated, where each of the objective functions contains a support function of a compact convex set. We identify a function lying exclusively in the class of higher-order K-?-convex and not in the class of K-?-bonvex function already existing in literature. Weak, strong and converse duality theorems are then established under higher-order K-?-convexity assumptions. Self duality is obtained by assuming the functions involved to be skew-symmetric. Several known results are also discussed as special cases.

scholarly journals Optimality and duality for nonsmooth semi-infinite E-convex multi-objective programming with support functions

2020 ◽  
Vol 11 ◽  
pp. 17
Author(s):  
Tarek Emam
Keyword(s):  
Strong Duality ◽  
Sufficient Optimality Conditions ◽  
Convex Programming Problem ◽  
Duality Theorems ◽  
Support Functions ◽  
Primal Problem ◽  
Multi Objective ◽  
Multi Objective Programming ◽  
Optimality And Duality ◽  
Convexity Assumptions

In this paper, we study a nonsmooth semi-infinite multi-objective E-convex programming problem involving support functions. We derive sufficient optimality conditions for the primal problem. We formulate Mond-Weir type dual for the primal problem and establish weak and strong duality theorems under various generalized E-convexity assumptions.

scholarly journals Symmetric duality in complex spaces over cones

2021 ◽  
pp. 4-4
Author(s):  
Izhar Ahmad ◽  
Divya Agarwal ◽  
Kumar Gupta
Keyword(s):  
Mathematical Programming ◽  
Duality Theory ◽  
Optimization Theory ◽  
Second Order ◽  
Symmetric Duality ◽  
Polyhedral Cones ◽  
Complex Spaces ◽  
Duality Results ◽  
Duality Relations

Duality theory plays an important role in optimization theory. It has been extensively used for many theoretical and computational problems in mathematical programming. In this paper duality results are established for first and second order Wolfe and Mond-Weir type symmetric dual programs over general polyhedral cones in complex spaces. Corresponding duality relations for nondifferentiable case are also stated. This work will also remove inconsistencies in the earlier work from the literature.

scholarly journals On duality theory for multiobjective semi-infinite fractional optimization model using higher order convexity.

2021 ◽  
Author(s):  
Tamanna Yadav ◽  
S. K. Gupta
Keyword(s):  
Optimization Model ◽  
Higher Order ◽  
Support Functions ◽  
Duality Results ◽  
Fractional Optimization ◽  
Different Types ◽  
Convexity Assumptions ◽  
Higher Order Equation ◽  
Higher Order Convexity ◽  
Dual Models

In the article, a semi-infinite fractional optimization model having multiple objectives is first formulated. Due to the presence of support functions in each numerator and denominator with constraints, the model so constructed is also non-smooth. Further, three different types of dual models viz Mond -Weir, Wolfe  and  Schaible  are presented and then usual duality results are proved using higher-order [[EQUATION]]   convexity assumptions. To show the existence of such generalized convex  functions, a nontrivial example has also been exemplified. Moreover, numerical examples have been  illustrated at suitable places to justify various results presented in the paper. The formulation and duality results discussed also generalize the well known results appeared in the literature.

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 Mond-Weir type second order multiobjective mixed symmetric duality with square root term under generalized univex function

2013 ◽  
Vol 4 (1) ◽  
pp. 21-33
Author(s):  
Arun Kumar Tripathy
Keyword(s):  
Second Order ◽  
Nondifferentiable Programming ◽  
Square Root ◽  
Symmetric Duality ◽  
New Class ◽  
Duality Results ◽  
Special Cases ◽  
Mild Assumption ◽  
Root Term

In this paper, a new class of second order (Φ,ρ)-univex and second order (Φ,ρ)-pseudo univex function are introduced with example. A pair Mond-Weir type second order mixed symmetric duality for multiobjective nondifferentiable programming is formulated and the duality results are established under the mild assumption of second order (∅,ρ) univexity and second order pseudo univexity. Special cases are discussed to show that this study extends some of the known results in related domain..

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 Multiobjective Fractional Programming Involving Generalized Semilocally V-Type I-Preinvex and Related Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Hachem Slimani ◽  
Shashi Kant Mishra
Keyword(s):  
Fractional Programming ◽  
Inequality Constraints ◽  
Strong Duality ◽  
Multiple Objective ◽  
Type I ◽  
Multiobjective Fractional Programming ◽  
Duality Results ◽  
Preinvex Functions ◽  
Necessary And Sufficient ◽  
Efficiency Conditions

We study a nonlinear multiple objective fractional programming with inequality constraints where each component of functions occurring in the problem is considered semidifferentiable along its own direction instead of the same direction. New Fritz John type necessary and Karush-Kuhn-Tucker type necessary and sufficient efficiency conditions are obtained for a feasible point to be weakly efficient or efficient. Furthermore, a general Mond-Weir dual is formulated and weak and strong duality results are proved using concepts of generalized semilocally V-type I-preinvex functions. This contribution extends earlier results of Preda (2003), Mishra et al. (2005), Niculescu (2007), and Mishra and Rautela (2009), and generalizes results obtained in the literature on this topic.

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.

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