• Communications of the Korean Mathematical Society
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• v.27 no.2
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• pp.411-423
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• 2012

A nondifferentiable nonlinear semi-infinite programming problem is considered, where the functions involved are ${\eta}$-semidifferentiable type I-preinvex and related functions. Necessary and sufficient optimality conditions are obtained for a nondifferentiable nonlinear semi-in nite programming problem. Also, a Mond-Weir type dual and a general Mond-Weir type dual are formulated for the nondifferentiable semi-infinite programming problem and usual duality results are proved using the concepts of generalized semilocally type I-preinvex and related functions.

• 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 the Korean Society for Precision Engineering
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• v.19 no.11
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• pp.137-145
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• 2002

Electric vehicle body has to be subjected to uniform load and requires auxiliary equipment such as air pipe and electric wire pipe. Especially, the cross beam supports the weight of passenger and electrical equipments. a lightweight vehicle body is salutary to save operating costs and fuel consumption. Therefore this study is to perform the size and the shape optimization of crossbeam for electric vehicle using the method of topology optimization to introduce the concept of homogenization based on optimality criteria method which is efficient for the problem having the number of design variables and a few boundary condition. this provides the method to determine the optimum position and shape of circular hole in the cross beam and then can achieve the optimal design to reduce weight.

• Journal of the Korean Mathematical Society
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• v.37 no.4
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• pp.625-643
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• 2000

In this paper we formulate an optimal control problem governed by time-delay Volterra integral equations; the problem includes control constraints as well as terminal equality and inequality constraints on the terminal state variables. First, using a special type of state and control variations, we represent a relatively simple and self-contained method for deriving new necessary conditions in the form of Pontryagin minimum principle. We show that these results immediately yield classical Pontryagin necessary conditions for control processes governed by ordinary differential equations (with or without delay). Next, imposing suitable convexity conditions on the functions involved, we derive Mangasarian-type and Arrow-type sufficient optimality conditions.

• Journal of Soil and Groundwater Environment
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• v.18 no.2
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• pp.45-53
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• 2013

Many cases of strategically designed groundwater remediation have lack of information of hydraulic conductivity or permeability, which can render remediation methods inefficient. Many studies have been carried out to minimize this shortcoming by determining detailed hydraulic information either through direct or indirect measurements. One popular method for hydraulic characterization is the pilot point method (PPM), where the hydraulic property is estimated at a small number of strategically selected points using secondary measurements such as hydraulic head or tracer concentration. This paper adopted a D-optimality based pilot point method (DBM) developed previously for hydraulic head measurements and extended it to include both hydraulic head and tracer measurements. Based on different combinations of trials, our analysis showed that DBM performs well when hydraulic head is used for pilot point selection and both hydraulic head and tracer measurements are used for determining the conductivity values.

• East Asian mathematical journal
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• v.33 no.1
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• pp.83-102
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• 2017

The main purpose of this paper is to introduce a pair new class of primal and dual problem associated with an operator. We prove the sufficient optimality theorem, weak duality theorem and strong duality theorem for these problems. The equivalence between the generalized optimization problems and the generalized variational inequality problems is studied in ordered topological vector space modeled in Hilbert spaces. We introduce the concept of partial differential associated (PDA)-operator, PDA-vector function and PDA-antisymmetric function to show the existence of a new class of function called, ($T_{\eta};{\xi}_{\theta}$)-invex functions. We discuss first and second kind of ($T_{\eta};{\xi}_{\theta}$)-invex functions and establish their existence theorems in ordered topological vector spaces.

• The Korean Journal of Applied Statistics
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• v.23 no.2
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• pp.285-293
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• 2010

The traditional methods for evaluating response surface designs are alphabetic optimality criteria. These single-number criteria such as D-, A-, G- and V-optimality do not completely reflect the prediction variance characteristics of the design in question. Alternatives to single-numbers summaries include graphical displays of the prediction variance across the design regions. We can suggest the animated quantile plots as the animation of the quantile plots and use these animated quantile plots for comparing and evaluating response surface designs.

• Transactions of the Korean Society of Automotive Engineers
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• v.7 no.8
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• pp.224-232
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• 1999

Topology optimization has evolved into a very efficient concept design tool and has been incorporated into design engineering processes in many industrial sectors. In recent years, topology optimization has become the focus of structural design community and has been researched and applied widely both in academia and industry. There are mainly tow approaches for topology optimization of continuum structures ; homogenization and density methods. The homogenization method is to compute is to compute an optimal distribution of microstructures in a given design domain. The sizes of the micro-calvities are treated as design variables for the topology optimization problem. the density method is to compute an optimal distribution of an isotropic material, where the material densities are treated as design variables. In this paper, the density method is used to formulate the topology optimization problem. This optimization problem is solved by using an optimality criteria method. Several example problems are solved to show the usefulness of the present approach.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.30 no.2B
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• pp.21-26
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• 2005

A routing algorithm using the Hopfield Neural Netork (HNN) is proposed in this paper. The proposed algorithm modifies the energy function for achieving the optimality of the solution and higher convergence rate. Experimental results show that the proposed algorithm outperforms convensional methods both in optimality and convergence.

• Korean Journal of Mathematics
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• v.30 no.3
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• pp.475-489
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• 2022

This paper focuses on a robust semi-infinite interval-valued optimization problem with uncertain inequality constraints (RSIIVP). By employing the concept of LU-optimal solution and Extended Mangasarian-Fromovitz Constraint Qualification (EMFCQ), necessary optimality conditions are established for (RSIIVP) and then sufficient optimality conditions for (RSIIVP) are derived, by using the tools of convexity. Moreover, a Wolfe type dual problem for (RSIIVP) is formulated and usual duality results are discussed between the primal (RSIIVP) and its dual (RSIWD) problem. The presented results are demonstrated by non-trivial examples.