Nondifferentiable Symmetric Duality Research Articles

A class of new type unified non-differentiable higher order symmetric duality theorems over arbitrary cones under generalized assumptions

In the present paper, a newly combined higher-order non-differentiable symmetric duality in scalar-objective programming over arbitrary cones is formulated. In literature we have discussed primal-dual results with arbitrary cones, while in this article, we have derived combined result with one model over arbitrary cones. The theorems of duality are derived for these problems under ?-pseudoinvexity/?-invexity/C-pseudoconvexity/C-convexity speculations over arbitrary cones.

A class of second order nondifferentiable symmetric duality relations under generalized assumptions

A class of second order nondifferentiable symmetric duality relations under generalized assumptions

Special Class of Second-Order Non-Differentiable Symmetric Duality Problems with (G,αf)-Pseudobonvexity Assumptions

In this paper, we introduce the various types of generalized invexities, i.e., α f -invex/ α f -pseudoinvex and ( G , α f ) -bonvex/ ( G , α f ) -pseudobonvex functions. Furthermore, we construct nontrivial numerical examples of ( G , α f ) -bonvexity/ ( G , α f ) -pseudobonvexity, which is neither α f -bonvex/ α f -pseudobonvex nor α f -invex/ α f -pseudoinvex with the same η . Further, we formulate a pair of second-order non-differentiable symmetric dual models and prove the duality relations under α f -invex/ α f -pseudoinvex and ( G , α f ) -bonvex/ ( G , α f ) -pseudobonvex assumptions. Finally, we construct a nontrivial numerical example justifying the weak duality result presented in the paper.

A New Approach on Mixed-Type Nondifferentiable Higher-Order Symmetric Duality

In this paper, a new mixed-type higher-order symmetric duality in scalar-objective programming is formulated. In the literature we have results either Wolfe or Mond–Weir-type dual or separately, while in this we have combined those results over one model. The weak, strong and converse duality theorems are proved for these programs under $$\eta $$ -invexity/ $$\eta $$ -pseudoinvexity assumptions. Self-duality is also discussed. Our results generalize some existing dual formulations which were discussed by Agarwal et al. (Generalized second-order mixed symmetric duality in nondifferentiable mathematical programming. Abstr. Appl. Anal. 2011. https://doi.org/10.1155/2011/103597 ), Chen (Higher-order symmetric duality in nonlinear nondifferentiable programs), Gulati and Gupta (Wolfe type second order symmetric duality in nondifferentiable programming. J. Math. Anal. Appl. 310, 247–253, 2005, Higher order nondifferentiable symmetric duality with generalized F-convexity. J. Math. Anal. Appl. 329, 229–237, 2007), Gulati and Verma (Nondifferentiable higher order symmetric duality under invexity/generalized invexity. Filomat 28(8), 1661–1674, 2014), Hou and Yang (On second-order symmetric duality in nondifferentiable programming. J Math Anal Appl. 255, 488–491, 2001), Verma and Gulati (Higher order symmetric duality using generalized invexity. In: Proceeding of 3rd International Conference on Operations Research and Statistics (ORS). 2013. https://doi.org/10.5176/2251-1938_ORS13.16 , Wolfe type higher order symmetric duality under invexity. J Appl Math Inform. 32, 153–159, 2014).

Wolfe Type Second Order Nondifferentiable Symmetric Duality in Multiobjective Programming over Cone with Generalized (K, F)-Convexity

A new class of second order (K, F) pseudoconvex function is introduced with example. A pair of Wolfe type second order nondifferentiable symmetric dual programs over arbitrary cones with square root term is formulated. The duality results are established under second order (K, F) pseudoconvexity assumption. Also a Wolfe type second order minimax mixed integer programming problem is formulated and the symmetric duality results are established under second order (K, F) pseudoconvexity assumption.

Strong duality theorem for multiobjective higher order nondifferentiable symmetric dual programs

In this paper, we establish a strong duality theorem for Mond-Weir type multiobjective higher order nondifferentiable symmetric dual programs. Our works correct some deficiencies in recent papers [higher-order symmetric duality in nondifferentiable multiobjective programming problems, J. Math. Anal. Appl. 290(2004)423-435] and [A note on higher-order nondifferentiable symmetric duality in multiobjective programming, Appl. Math. Letters 24(2011) 1308-1311].

A note on higher-order nondifferentiable symmetric duality in multiobjective programming

In this work, we establish a strong duality theorem for Mond–Weir type multiobjective higher-order nondifferentiable symmetric dual programs. This fills some gaps in the work of Chen [X. Chen, Higher-order symmetric duality in nondifferentiable multiobjective programming problems, J. Math. Anal. Appl. 290 (2004) 423–435].

Non-differentiable symmetric duality for multiobjective programming with cone constraints

Abstract Two pairs of non-differentiable multiobjective symmetric dual problems with cone constraints over arbitrary cones, which are Wolfe type and Mond–Weir type, are considered. On the basis of weak efficiency with respect to a convex cone, we obtain symmetric duality results for the two pairs of problems under cone-invexity and cone-pseudoinvexity assumptions on the involved functions. Our results extend the results in Khurana [S. Khurana, Symmetric duality in multiobjective programming involving generalized cone-invex functions, European Journal of Operational Research 165 (2005) 592–597] to the non-differentiable multiobjective symmetric dual problem.

Higher-order nondifferentiable symmetric duality with generalized F-convexity

A pair of nondifferentiable higher-order Wolfe type symmetric dual models is formulated and usual duality theorems are established under higher-order F-convexity assumption. Symmetric minimax mixed integer primal and dual problems are also discussed.

A note on nondifferentiable symmetric duality

Under suitable hypotheses on the function f, the two constrained minimization problems:are well known each to be dual to the other. This symmetric duality result is now extended to a class of nonsmooth problems, assuming some convexity hypotheses. The first problem is generalized to:in which T and S are convex cones, S* is the dual cone of S, and ∂y denotes the subdifferential with respect to y. The usual method of proof uses second derivatives, which are no longer available. Therefore a different method is used, where a nonsmooth problem is approximated by a sequence of smooth problems. This duality result confirms a conjecture by Chandra, which had previously been proved only in special cases.