• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.4 no.2
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• pp.59-66
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• 2000

We consider a multiobjective fractional variational programming problem (P) involving vector valued functions. By using the concept of proper efficiency, a relationship between the primal problem and parametric multiobjective variational problem is indicated.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.281-292
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• 2007

A pair of symmetric fractional variational programming problems is formulated over cones. Weak, strong, converse and self duality theorems are discussed under pseudoinvexity. Static symmetric dual fractional programs are included as special case and corresponding symmetric duality results are merely stated.

• 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.27 no.1_2
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• pp.245-257
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• 2009

A mixed type dual for multiobjective variational problem involving higher order derivatives is formulated and various duality results under generalized invexity are established. Special cases are generated and it is also pointed out that our results can be viewed as a dynamic generalization of existing results in the static programming.

• Structural Engineering and Mechanics
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• v.23 no.4
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• pp.431-447
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• 2006

A new incremental finite element model is developed to simulate the frictional contact of elastic bodies. The incremental convex programming method is exploited, in the framework of finite element approach, to recast the variational inequality principle of contact problem in a discretized form. The non-classical friction model of Oden and Pires is adopted, however, the friction effect is represented by an equivalent non-linear stiffness rather than additional constraints. Different parametric studies are worked out to address the versatility of the proposed model.

• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.123-137
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• 2009

A multiobjective variational problem involving higher order derivatives is considered and Fritz-John and Karush-Kuhn-Tucker type optimality conditions for this problem are derived. As an application of Karush-Kuhn-Tucker optimality conditions, Wolfe type dual to this variational problem is constructed and various duality results are validated under generalized invexity. Some special cases are mentioned and it is also pointed out that our results can be considered as a dynamic generalization of the already existing results in nonlinear programming.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.433-455
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• 2005

Fritz John, and Karush-Kuhn-Tucker type optimality conditions for a constrained variational problem involving higher order derivatives are obtained. As an application of these Karush-Kuhn-Tucker type optimality conditions, Wolfe and Mond-Weir type duals are formulated, and various duality relationships between the primal problem and each of the duals are established under invexity and generalized invexity. It is also shown that our results can be viewed as dynamic generalizations of those of the mathematical programming already reported in the literature.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.7 no.2
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• pp.83-94
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• 2003

Let K be a nonempty closed convex subset of a real Hilbert space H. Approximation solvability of a system of nonlinear variational inequality (SNVI) problems, based on the convergence of projection methods, is given as follows: find elements $x^*,\;y^*{\in}H$ such that $g(x^*),\;g(y^*){\in}K$ and $$<\;{\rho}T(y^*)+g(x^*)-g(y^*),\;g(x)-g(x^*)\;{\geq}\;0\;{\forall}\;g(x){\in}K\;and\;for\;{\rho}>0$$ $$<\;{\eta}T(x^*)+g(y^*)-g(x^*),\;g(x)-g(y^*)\;{\geq}\;0\;{\forall}g(x){\in}K\;and\;for\;{\eta}>0,$$ where T: $H\;{\rightarrow}\;H$ is a relaxed $g-{\gamma}-r-cocoercive$ and $g-{\mu}-Lipschitz$ continuous nonlinear mapping on H and g: $H{\rightarrow}\;H$ is any mapping on H. In recent years general variational inequalities and their algorithmic have assumed a central role in the theory of variational methods. This two-step system for nonlinear variational inequalities offers a great promise and more new challenges to the existing theory of general variational inequalities in terms of applications to problems arising from other closely related fields, such as complementarity problems, control and optimizations, and mathematical programming.

• Nonlinear Functional Analysis and Applications
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• v.26 no.2
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• pp.347-371
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• 2021

A plethora of applications from mathematical programmings, such as minimax, mathematical programming, penalization and fixed point problems can be framed as variational inequality problems. Most of the methods that used to solve such problems involve iterative methods, that is why, in this paper, we introduce a new extragradient-like method to solve pseudomonotone variational inequalities in a real Hilbert space. The proposed method has the advantage of a variable step size rule that is updated for each iteration based on previous iterations. The main advantage of this method is that it operates without the previous knowledge of the Lipschitz constants of an operator. A strong convergence theorem for the proposed method is proved by letting the mild conditions on an operator 𝒢. Numerical experiments have been studied in order to validate the numerical performance of the proposed method and to compare it with existing methods.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.61-74
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• 2011

In this paper, we introduce a new iteration method based on the hybrid method in mathematical programming and the descent-like method for finding a common element of the solution set for a variational inequality and the set of common fixed points of a nonexpansive semigroup in Hilbert spaces. We obtain a strong convergence for the sequence generated by our method in Hilbert spaces. The result in this paper modifies and improves some well-known results in the literature for a more general problem.