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 Nondifferentiable higher order symmetric duality under invexity/generalized invexity

Filomat ◽  
2014 ◽  
Vol 28 (8) ◽  
pp. 1661-1674 ◽  
Author(s):  
T.R. Gulati ◽  
Khushboo Verma
Keyword(s):  
Higher Order ◽  
Duality Theorems ◽  
Symmetric Duality ◽  
Converse Duality ◽  
Generalized Invexity ◽  
Self Duality ◽  
Special Cases ◽  
Dual Models

In this paper, we introduce a pair of nondifferentiable higher-order symmetric dual models. Weak, strong and converse duality theorems for this pair are established under the assumption of higher order invexity/generalized invexity. Self duality has been discussed assuming the function involved to be skew-symmetric. Several known results are obtained as special cases.

scholarly journals Symmetric duality for Bonvex multiobjective fractional continuous time programming problems

2010 ◽  
Vol 7 (2) ◽  
pp. 413-424
Author(s):  
Deo Brat Ojha
Keyword(s):  
Continuous Time ◽  
Efficient Solutions ◽  
Weak Duality ◽  
Duality Theorems ◽  
Symmetric Duality ◽  
Converse Duality ◽  
Multi Objective ◽  
Properly Efficient Solutions ◽  
Self Duality ◽  
Duality Relations

We introduced a symmetric dual for multi objective fractional variational programs in second order. Under invexity assumptions, we established weak, strong and converse duality as well as self duality relations .We work with properly efficient solutions in strong and converse duality theorems. The weak duality theorems involves efficient solutions .

scholarly journals Mixed type second-order symmetric duality under F-convexity

2012 ◽  
Vol 3 (1) ◽  
pp. 1-5 ◽  
Author(s):  
Tilak Raj GULATI ◽  
Khushboo VERMA
Keyword(s):  
Mixed Type ◽  
Second Order ◽  
Duality Theorems ◽  
Symmetric Duality ◽  
Converse Duality ◽  
Dual Problems ◽  
Second Order Symmetric Duality ◽  
Convexity Assumptions

We introduce a pair of second order mixed symmetric dual problems. Weak, strong and converse duality theorems for this pair are established under $F-$convexity assumptions.

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 Nondifferentiable G-Mond–Weir Type Multiobjective Symmetric Fractional Problem and Their Duality Theorems under Generalized Assumptions

Symmetry ◽  
2019 ◽  
Vol 11 (11) ◽  
pp. 1348 ◽  
Author(s):  
Ramu Dubey ◽  
Lakshmi Narayan Mishra ◽  
Luis Manuel Sánchez Ruiz
Keyword(s):  
Vector Optimization ◽  
Optimization Problem ◽  
Vector Optimization Problem ◽  
Second Order ◽  
Type Model ◽  
Dual Model ◽  
Duality Theorems ◽  
Converse Duality ◽  
Numerical Example ◽  
Primal Dual

In this article, a pair of nondifferentiable second-order symmetric fractional primal-dual model (G-Mond–Weir type model) in vector optimization problem is formulated over arbitrary cones. In addition, we construct a nontrivial numerical example, which helps to understand the existence of such type of functions. Finally, we prove weak, strong and converse duality theorems under aforesaid assumptions.

scholarly journals Mixed type symmetric and self duality for multiobjective variational problems with support functions

2013 ◽  
Vol 23 (3) ◽  
pp. 387-417
Author(s):  
I. Husain ◽  
Rumana Mattoo
Keyword(s):  
Mixed Type ◽  
Variational Problems ◽  
Kernel Functions ◽  
Boundary Values ◽  
Natural Boundary ◽  
Duality Theorems ◽  
Support Functions ◽  
Self Duality ◽  
Multiobjective Nonlinear Programming ◽  
Multiobjective Variational Problems

In this paper, a pair of mixed type symmetric dual multiobjective variational problems containing support functions is formulated. This mixed formulation unifies two existing pairs Wolfe and Mond-Weir type symmetric dual multiobjective variational problems containing support functions. For this pair of mixed type nondifferentiable multiobjective variational problems, various duality theorems are established under convexity-concavity and pseudoconvexity-pseudoconcavity of certain combination of functionals appearing in the formulation. A self duality theorem under additional assumptions on the kernel functions that occur in the problems is validated. A pair of mixed type nondifferentiable multiobjective variational problem with natural boundary values is also formulated to investigate various duality theorems. It is also pointed that our duality theorems can be viewed as dynamic generalizations of the corresponding (static) symmetric and self duality of multiobjective nonlinear programming with support functions.

Second-Order Symmetric Duality in Variational Control Problems Over Cone Constraints

2018 ◽  
Vol 35 (04) ◽  
pp. 1850028
Author(s):  
Anurag Jayswal ◽  
Shalini Jha ◽  
Ashish Kumar Prasad ◽  
Izhar Ahmad
Keyword(s):  
Duality Theorem ◽  
Second Order ◽  
Control Problems ◽  
Duality Theorems ◽  
Symmetric Duality ◽  
Control Programs ◽  
Convexity Assumption ◽  
Self Duality ◽  
Cone Constraints ◽  
Second Order Symmetric Duality

In the present paper, we introduce a pair of multiobjective second-order symmetric variational control programs over cone constraints and derive weak, strong and converse duality theorems under second-order [Formula: see text]-convexity assumption. Moreover, self-duality theorem is also discussed. Our results extend some of the known results in literature.

NONDIFFERENTIABLE SECOND-ORDER SYMMETRIC DUALITY

2005 ◽  
Vol 22 (01) ◽  
pp. 19-31 ◽  
Author(s):  
I. AHMAD ◽  
Z. HUSAIN
Keyword(s):  
Strong Duality ◽  
Second Order ◽  
Mixed Integer ◽  
Duality Theorems ◽  
Symmetric Duality ◽  
Dual Problems ◽  
Self Duality ◽  
Second Order Symmetric Duality ◽  
Primal And Dual Problems ◽  
Primal And Dual

A pair of Mond–Weir type nondifferentiable second-order symmetric primal and dual problems in mathematical programming is formulated. Weak duality, strong duality, and converse duality theorems are established under η-pseudobonvexity assumptions. Symmetric minimax mixed integer primal and dual problems are also investigated. Moreover, the self duality theorem is also discussed.

scholarly journals Generalized Second-Order Mixed Symmetric Duality in Nondifferentiable Mathematical Programming

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
Ravi P. Agarwal ◽  
Izhar Ahmad ◽  
S. K. Gupta ◽  
N. Kailey
Keyword(s):  
Mathematical Programming ◽  
Second Order ◽  
Duality Theorems ◽  
Symmetric Duality ◽  
Converse Duality ◽  
Nondifferentiable Functions

This paper is concerned with a pair of second-order mixed symmetric dual programs involving nondifferentiable functions. Weak, strong, and converse duality theorems are proved for aforementioned pair using the notion of second-orderF-convexity/pseudoconvexity assumptions.

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