• East Asian mathematical journal
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• v.31 no.3
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• pp.345-349
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• 2015

In this paper, we consider a fractional robust optimization problem (FP) and give necessary optimality theorems for (FP). Establishing a nonfractional optimization problem (NFP) equivalent to (FP), we formulate a Mond-Weir type dual problem for (FP) and prove duality theorems for (FP).

• East Asian mathematical journal
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• v.31 no.5
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• pp.737-742
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• 2015

In this paper, we consider a generalized fractional robust optimization problem (FP). Establishing a nonfractional optimization problem (NFP) equivalent to (FP), we establish necessary optimality conditions and duality results.

• Journal of applied mathematics & informatics
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• v.11 no.1_2
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• pp.273-281
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• 2003

The purpose of this paper is to study the duality theorems in cone constrained multiobjective nonlinear programming for pseudo-invex objectives and quasi-invex constrains and the constraint cones are arbitrary closed convex ones and not necessarily the nonnegative orthants.

• Communications of the Korean Mathematical Society
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• v.19 no.1
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• pp.179-196
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• 2004

Mond-Weir type duals for multiobjective variational problems are formulated. Under generalized vector variational type I invexity assumptions on the functions involved, sufficient optimality conditions, weak and strong duality theorems are proved efficient and properly efficient solutions of the primal and dual problems.

• Journal of applied mathematics & informatics
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• v.26 no.5_6
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• pp.819-837
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• 2008

A mixed type dual to the control problem in order to unify Wolfe and Mond-Weir type dual control problem is presented in various duality results are validated and the generalized invexity assumptions. It is pointed out that our results can be extended to the control problems with free boundary conditions. The duality results for nonlinear programming problems already existing in the literature are deduced as special cases of our results.

• Journal of applied mathematics & informatics
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• v.26 no.1_2
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• pp.251-261
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• 2008

In this paper second order cone convex, second order cone pseudoconvex, second order strongly cone pseudoconvex and second order cone quasiconvex functions are introduced and their interrelations are discussed. Further a MondWeir Type second order dual is associated with the Vector Minimization Problem and the weak and strong duality theorems are established under these new generalized convexity assumptions.

• East Asian mathematical journal
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• v.33 no.3
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• pp.265-269
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• 2017

In this paper, we formulate a sufficient optimality theorem for the robust optimization problem (UP) under (V, ${\rho}$)-invexity assumption. Moreover, we formulate a Mond-Weir type dual problem for the robust optimization problem (UP) and show that the weak and strong duality hold between the primal problems and the dual problems.

• Journal of applied mathematics & informatics
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• v.32 no.3_4
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• pp.491-502
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• 2014

In this paper, by using the notion of ${\rho}$-(p,r)-invexity assumptions on the functions involved, optimality conditions and duality results (Mond-Weir, Wolfe and mixed type) are established on differentiable manifolds. Counterexample is constructed to justify that our investigations are more general than the existing work available in the literature.

• East Asian mathematical journal
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• v.32 no.5
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• pp.635-639
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• 2016

In this paper, we prove a sufficient optimality theorems for the problem(FP) under(V, ${\rho}$)-invexity assumption. And we give Mond-Weir type dual problem and proved weak and strong duality theorem under (V, ${\rho}$)-invexity

• Journal of applied mathematics & informatics
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• v.35 no.1_2
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• pp.147-163
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• 2017

In this paper, we establish the necessary and sufficient Karush-Kuhn-Tucker (KKT) conditions for an optimization problem with difference of set-valued maps under generalized cone convexity assumptions. We also study the duality results of Mond-Weir (MW D), Wolfe (W D) and mixed (Mix D) types for the weak solutions of the problem (P).