• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.149-159
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• 2009

In this paper, we introduce some approximate optimal solutions and an augmented Lagrangian function in nonlinear programming, establish dual function and dual problem based on the augmented Lagrangian function, discuss the relationship between the approximate optimal solutions of augmented Lagrangian problem and that of primal problem, obtain approximate KKT necessary optimality condition of the augmented Lagrangian problem, prove that the approximate stationary points of augmented Lagrangian problem converge to that of the original problem. Our results improve and generalize some known results.

• Bulletin of the Korean Mathematical Society
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• v.55 no.3
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• pp.749-762
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• 2018

In this paper, the new optimal perturbation iteration method has been applied to solve the generalized regularized long wave equation. Comparing the new analytic approximate solutions with the known exact solutions reveals that the proposed technique is extremely accurate and effective in solving nonlinear wave equations. We also show that,unlike many other methods in literature, this method converges rapidly to exact solutions at lower order of approximations.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1249-1262
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• 2010

An approximate alternating linearization decomposition method, for minimizing the sum of two convex functions with some separable structures, is presented in this paper. It can be viewed as an extension of the method with exact solutions proposed by Kiwiel, Rosa and Ruszczynski(1999). In this paper we use inexact optimal solutions instead of the exact ones that are not easily computed to construct the linear models and get the inexact solutions of both subproblems, and also we prove that the inexact optimal solution tends to proximal point, i.e., the inexact optimal solution tends to optimal solution.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.24 no.3
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• pp.302-307
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• 2015

The automobile is an important means of transportation. For this reason, the automotive wheel is also an important component in the automotive industry because it acts as a load support and is closely related to safety. Thus, the wheel design is a very important safety aspect. In this paper, an optimal design for minimizing automotive wheel stress and increasing wheel safety is described. To study the optimal design, a central composite design (CCD) and D-optimal design theory are applied, and the approximate function using the response surface method (RSM) is generated. The optimal solutions using the non-dominant sorting genetic algorithm (NSGA-II) are then derived. Comparing CCD and D-optimal solution accuracy and verified the CCD can deduce more accuracy optimal solutions.

• The KIPS Transactions:PartC
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• v.14C no.2
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• pp.179-184
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• 2007

The problem of selecting base station location in the design of mobile communication system has been basically regarded as a problem of assigning maximum users in the cell to the minimum base stations while maintaining minimum SIR. and it is NP hard. The objective function of warehouse location problem, which has been used by many researchers, is not proper function in the base station location problem in CDMA mobile communication, The optimal and approximate solutions have been presented by using proposed object function and algorithms of exact solution, and the simulation results have been assessed and analyzed. The optimal and approximate solutions are found by using mixed integer programming instead of meta-heuristic search methods.

• The Journal of Information Systems
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• v.17 no.3
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• pp.39-58
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• 2008

Mixed Chinese Postman Problem (MCPP) is a practical generalization of the classical Chinese Postman Problem (CPP) and it could be applied in many real world. Although MCPP is useful in terms of reality, MCPP has been proved to be a NP-complete problem. To find optimal solutions efficiently in MCPP, we can reduce searching space to be small effective searching space containing optimal solutions. We propose GENIIS methodology, which is a kind of hybrid algorithm combines the approximate algorithms and genetic algorithm. To get good solutions in the effective searching space, GENIIS uses approximate algorithm and genetic algorithm. This paper validates the usefulness of the proposed approach in a simulation. The results of our paper could be utilized to increase the efficiencies of network and transportation in business.

• Journal of the Korean Society for Precision Engineering
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• v.32 no.9
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• pp.815-824
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• 2015

In this study, we conducted the approximate multi-objective optimization of gap sizes of pressurized-water reactor (PWR) annular fuels. To determine the contacting tendency of the inner-outer gaps between the annular fuel pellets and cladding, thermoelastic-plastic-creep (TEPC)analysis of PWR annular fuels was performed, using in-house FE code. For the efficient heat transfer at certain levels of stress, we investigated the tensile, compressive hoop stress and temperature, and optimized the gap sizes using the non-dominant sorting genetic algorithm (NSGA-II). For this, response surface models of objective and constraint functions were generated, using central composite (CCD) and D-optimal design. The accuracy of approximate models was evaluated through $R^2$ value. The obtained optimal solutions by NSGA-II were verified through the TEPC analysis, and we compared the obtained optimum solutions and generated errors from the CCD and D-optimal design. We observed that optimum solutions differ, according to design of experiments (DOE) method.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2007.04a
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• pp.141-144
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• 2007

Given a number of training data, a traditional BPN is normally trained by minimizing the absolute difference between target outputs and approximate outputs. When BPN is used as a meta-model for inequality constraint function, approximate optimal solutions are sometimes actually infeasible in a case where they are active at the constraint boundary. The paper describes the development of the efficient BPN based meta-model that enhances the constraint feasibility of approximate optimal solution. The modified BPN based meta-model is obtained by including the decision condition between lower/upper bounds of a constraint and an approximate value. The proposed approach is verified through a simple mathematical function and a ten-bar planar truss problem.

• International Journal of Aeronautical and Space Sciences
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• v.3 no.2
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• pp.46-58
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• 2002

An inverse method is introduced to construct benchmark problems for the numerical solution of initial value problems. Benchmark problems constructed through this method have a known exact solution, even though analytical solutions are generally not obtainable. The solution is constructed such that it lies near a given approximate numerical solution, and therefore the special case solution can be generated in a versatile and physically meaningful fashion and can serve as a benchmark problem to validate approximate solution methods. A smooth interpolation of the approximate solution is forced to exactly satisfy the differential equation by analytically deriving a small forcing function to absorb all of the errors in the interpolated approximate solution. A multi-variable orthogonal function expansion method and computer symbol manipulation are successfully used for this process. Using this special case exact solution, it is possible to directly investigate the relationship between global errors of a candidate numerical solution process and the associated tuning parameters for a given code and a given problem. Under the assumption that the original differential equation is well-posed with respect to the small perturbations, we thereby obtain valuable information about the optimal choice of the tuning parameters and the achievable accuracy of the numerical solution. Illustrative examples show the utility of this method not only for the ordinary differential equations (ODEs) but for the partial differential equations (PDEs).

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.16 no.12
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• pp.1156-1166
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• 2004

The shape of plate-fin type heat sink is numerically optimized to acquire the minimum pressure drop under the required temperature rise. In constrained nonlinear optimization problems of thermal/fluid systems, three fundamental difficulties such as high computational cost for function evaluations (i.e., pressure drop and thermal resistance), the absence of design sensitivity information, and the occurrence of numerical noise are commonly confronted. Thus, a sequential approximate optimization (SAO) algorithm has been introduced because it is very hard to obtain the optimal solutions of fluid/thermal systems by means of gradient-based optimization techniques. In this study, the progressive quadratic response surface method (PQRSM) based on the trust region algorithm, which is one of sequential approximate optimization algorithms, is used for optimization and the heat sink is optimized by combining it with the computational fluid dynamics (CFD).