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

[EN] 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.Dubey, R.; Mishra, LN.; Sánchez Ruiz, LM. (2019). Nondifferentiable G-Mond-Weir Type Multiobjective Symmetric Fractional Problem and Their Duality Theorems under Generalized Assumptions. Symmetry (Basel). 11(11):1-18. https://doi.org/10.3390/sym11111348S118111

Second-order symmetric duality with cone constraints

AbstractWolfe and Mond–Weir type second-order symmetric duals are formulated and appropriate duality theorems are established under η-bonvexity/η-pseudobonvexity assumptions. This formulation removes several omissions in an earlier second-order primal dual pair introduced by Devi [Symmetric duality for nonlinear programming problems involving η-bonvex functions, European J. Oper. Res. 104 (1998) 615–621]

Generalized Second-Order G-Wolfe Type Fractional Symmetric Program and their Duality Relations under Generalized Assumptions

In this article, we formulate the concept of generalize bonvexity/pseudobonvexity functions. We formulate duality results for second-order fractional symmetric dual programs of G-Wolfe-type model. In the next section, we explain the duality theorems under generalize bonvexity/pseudobonvexity assumptions. We identify a function lying exclusively in the class of generalize pseudobonvex and not in class of generalize bonvex functions. Our results are more generalized several known results in the literature

Symmetric Duality in Mathematical Programming

N

Higher-order symmetric duality in nondifferentiable multiobjective programming problems

AbstractIn this paper, a pair of nondifferentiable multiobjective programming problems is first formulated, where each of the objective functions contains a support function of a compact convex set in Rn. For a differentiable function h:Rn×Rn→R, we introduce the definitions of the higher-order F-convexity (F-pseudo-convexity, F-quasi-convexity) of function f:Rn→R with respect to h. When F and h are taken certain appropriate transformations, all known other generalized invexity, such as η-invexity, type I invexity and higher-order type I invexity, can be put into the category of the higher-order F-invex functions. Under these the higher-order F-convexity assumptions, we prove the higher-order weak, higher-order strong and higher-order converse duality theorems related to a properly efficient solution

Duality in mathematical programming.

In this thesis entitled, “Duality in Mathematical Programming”, the emphasis is given on formulation and conceptualization of the concepts of second-order duality, second-order mixed duality, second-order symmetric duality in a variety of nondifferentiable nonlinear programming under suitable second-order convexity/second-order invexity and generalized second-order convexity / generalized second-order invexity. Throughout the thesis nondifferentiablity occurs due to square root function and support functions. A support function which is more general than square root of a positive definite quadratic form. This thesis also addresses second-order duality in variational problems under suitable second-order invexity/secondorder generalized invexity. The duality results obtained for the variational problems are shown to be a dynamic generalization for thesis of nonlinear programming problem.Digital copy of Thesis.University of Kashmir

Symmetric Duality for Mathematical Programming in Complex Spaces with Higher-Order F-univexity

Abstract: In this study, we established appropriate duality results for a pair of Wolfe and Mond-Weir type symmetric dual for nonlinear programming problems in complex spaces under higher order F-univexity, Funicavity/F-pseudounivexity, F-pseudounicavity. Results of this paper are real extension of previous literature