• Journal of the Chungcheong Mathematical Society
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• v.29 no.3
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• pp.465-475
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• 2016

We establish necessary and sufficient optimality conditions for a class of generalized nondifferentiable fractional optimization programming problems. Moreover, we prove the weak and strong duality theorems under (V, ${\rho}$)-invexity assumption.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1527-1534
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• 2010

In this paper, we consider nonsmooth optimization problem of which objective and constraint functions are locally Lipschitz. We establish sufficient optimality conditions and duality results for nonsmooth vector optimization problem given under nearly strict invexity and near invexity-infineness assumptions.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1535-1544
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• 2010

Sufficient optimality conditions for a class of generalized non-differentiable fractional optimization programming problems are established. Moreover, we prove the weak and strong duality theorems under (V, $\rho$)-invexity assumption.

• Proceedings of the Korean Reliability Society Conference
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• 2005.06a
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• pp.109-113
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• 2005

Optimality for block designs have received much attention in the literature. Here we review these criteria and present results showing their A,D and E connection. Also we acquainted with the mathematical methods of designing optimal experiments. In this paper, we will to do work about optimality in experimental designs.

• East Asian mathematical journal
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• v.35 no.3
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• pp.289-296
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• 2019

We establish necessary and sufficient optimality conditions for a nonsmooth fractional robust optimization programming problems. Moreover, we prove the weak and strong duality theorems under (V, ${\rho}$)-invexity assumption.

• East Asian mathematical journal
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• v.39 no.5
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• pp.505-514
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• 2023

In this paper, we consider a second-order cone linear fractional vector optimization problems (FVP), and obtain sequential optimality theorems for (FVP) which hold without any constraint qualification and which are expressed by sequences.

• Bulletin of the Korean Mathematical Society
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• v.51 no.1
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• pp.287-301
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• 2014

In this paper, we prove a necessary optimality theorem for a nonsmooth optimization problem in the face of data uncertainty, which is called a robust optimization problem. Recently, the robust optimization problems have been intensively studied by many authors. Moreover, we give examples showing that the convexity of the uncertain sets and the concavity of the constraint functions are essential in the optimality theorem. We present an example illustrating that our main assumptions in the optimality theorem can be weakened.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.597-610
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• 2010

For a class of nonlinear bilevel programming problems in which the follower's problem is linear, the paper develops a genetic algorithm based on the optimality conditions of linear programming. At first, we denote an individual by selecting a base of the follower's linear programming, and use the optimality conditions given in the simplex method to denote the follower's solution functions. Then, the follower's problem and variables are replaced by these optimality conditions and the solution functions, which makes the original bilevel programming become a single-level one only including the leader's variables. At last, the single-level problem is solved by using some classical optimization techniques, and its objective value is regarded as the fitness of the individual. The numerical results illustrate that the proposed algorithm is efficient and stable.

• Journal of the Korean Statistical Society
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• v.27 no.1
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• pp.133-152
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• 1998

The central composite design is widely used in the response surface analysis, because it can fit the second order model with small experimental points. In practice, the experimental data are not always obtained on all the points. When there are missing observations, many problems due to the missing cells can occur. In this paper, the influence of a missing cell on the central composite design is discussed. First, the influences of a missing cell on the variances of estimated regression coefficents are compared as $\alpha$ varies. Second, how the average predition variance is affected by a missing sell is discussed. And the influence on rotatability is investigated. Third, the influence of a missing cell on optimality, especially on D-optimality and A-optimality, is examined.

• 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.