• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1511-1523
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• 2011

In this paper, we consider the smoothing Newton method for the nonlinear complementarity problems with $P_0$-function. The proposed algorithm is based on a new smoothing function and it needs only to solve one linear system of equations and perform one line search per iteration. Under the condition that the solution set is nonempty and bounded, the proposed algorithm is proved to be convergent globally. Furthermore, the local superlinearly(quadratic) convergence is established under suitable conditions. Preliminary numerical results show that the proposed algorithm is very promising.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1995.09a
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• pp.211-219
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• 1995

블록-삼각(Block-angular)구조를 갖는 선형 제약식과 분리되지 않는 콘벡스 목적함수의 대규모 비분리 콘벡스 최적화 문제의 해법으로 번들-분해법 (Bundle Based Decomposition)을 이용한 알고리즘 SQA(Separable Quadratic Approximation)은 비분리 콘벡스 프로그램을 분리가능한 2차계획 법(Separable Quadratic Programming) 문제로 근사화시켜 번들-분해법을 축 차적으로 적용한다. 본 연구는 수렴성(local convergence & global convergence) 및 알고리즘 구현 [1]에 이어 이에 대한 수치적용 결과를 중심 으로 소개한다. 수치 적용은 ANSI C로 작성된 SQA 프로그램을 SUN SPARC II에서 실행하였으며 이때 대규모 비분리 최적화 문제의 비분리 목 적함수와 블록-삼각 구조의 선형 제약식들이 계수들은 ANSI C의 랜덤함수 로부터 임의의 값들을 이용하였다. 이와같은 다양한 비분리 콘벡스 최적화 문제에 대한 수렴성, 반복회수 및 처리시간등의 결과와 함께 GAMS/MINOS 의 최적해를 소개한다.

• Journal of the Korean Mathematical Society
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• v.45 no.5
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• pp.1275-1295
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• 2008

In this paper, we consider an impulsive nonlinear second order ordinary differential equation with nonlinear three-point boundary conditions and develop a monotone iteration scheme by relaxing the convexity assumption on the function involved in the differential equation and the concavity assumption on nonlinearities in the boundary conditions. In fact, we obtain monotone sequences of iterates (approximate solutions) converging quadratically to the unique solution of the impulsive three-point boundary value problem.

• Journal of the Korean Society of Industry Convergence
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• v.12 no.3
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• pp.149-155
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• 2009

A new finite element equation is derived by applying quadratic and cubic time integration scheme to the variational formulation in time-integral for the analysis of the transient elastodynamic problems to increase the numerical accuracy and stability. Emphasis is focused on methodology for cubic time integration scheme procedure which are never presented before. In this semidiscrete approximations of the field variables, the time axis is divided equally and quadratic and cubic time variation is assumed in those intervals, and space is approximated by the usual finite element discretization technique. It is found that unconditionally stable numerical results are obtained in case of the cubic time variation. Some numerical examples are given to show the versatility of the presented formulation.

• Journal of the Korean Mathematical Society
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• v.37 no.5
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• pp.822-822
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• 2000

• Proceedings of the KIEE Conference
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• 1988.07a
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• pp.87-90
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• 1988

This paper reports a simple posteriori error estimate method for adaptive finite element mesh generation using quadratic shape function especially for the magnetic field problems. The elements of quadratic shape function have more precise solution than those of linear shape function. Therefore, the difference of two solutions gives error quantity. The method uses the magnetic flux density error as a basis for refinement. This estimator is tested on two dimensional problem which has singular points. The estimated error is always under estimated but in same order as exact error, and this method is much simpler and more convenient than other methods. The result shows that the adaptive mesh gives even better rate of convergence in global error than the uniform mesh.

• East Asian mathematical journal
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• v.28 no.3
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• pp.293-303
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• 2012

Sequential quadratic programming (SQP) has been one of the most important methods for solving nonlinear constrained optimization problems. Recently, filter method, proposed by Fletcher and Leyffer, has been extensively applied for its promising numerical results. In this paper, we present and study an active set SQP-filter algorithm for inequality constrained optimization. The active set technique reduces the size of quadratic programming (QP) subproblem. While by the filter method, there is no penalty parameter estimate. Moreover, Maratos effect can be overcome by filter technique. Global convergence property of the proposed algorithm are established under suitable conditions. Some numerical results are reported in this paper.

• Journal of the Korean Mathematical Society
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• v.61 no.4
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• pp.621-657
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• 2024

In this study, the numerical solution of a space-fractional Burgers' equation with initial and boundary conditions is considered. This equation is the simplest nonlinear model for diffusive waves in fluid dynamics. It occurs in a variety of physical phenomena, including viscous sound waves, waves in fluid-filled viscous elastic pipes, magneto-hydrodynamic waves in a medium with finite electrical conductivity, and one-dimensional turbulence. The proposed QBS/CNG technique consists of the Galerkin method with a function basis of quadratic B-splines for the spatial discretization of the space-fractional Burgers' equation. This is then followed by the Crank-Nicolson approach for time-stepping. A linearized scheme is fully constructed to reduce computational costs. Stability analysis, error estimates, and convergence rates are studied. Finally, some test problems are used to confirm the theoretical results and the proposed method's effectiveness, with the results displayed in tables, 2D, and 3D graphs.

• Journal of Convergence for Information Technology
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• v.11 no.8
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• pp.207-211
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• 2021

This paper addresses a two-stage flexible flow shop scheduling problem in which there is one machine in stage 1 and two identical machines in stage 2. The objective is the minimization of the total completion time. The problem is formulated by a mixed integer quadratic programming (MIQP) and a hybrid simulated annealing (HSA) is proposed to solve the MIQP. The HSA adopts the exploration capabilities of a genetic algorithm and incorporates a simulated annealing to reduce the premature convergence. Extensive computational tests on randomly generated problems are carried out to evaluate the performance of the HSA.

• Journal of the Korean Society of Radiology
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• v.9 no.6
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• pp.417-420
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• 2015

We obtained Surviving Fraction (SF) after irradiation carbon beam to compare the applicability of the Linear-Quadratic model, Incomplete Repair model, Marchese model. Mathematica software(ver 9.0) used to calcurate parameters and compared result. LQ model could not explain the entire response of fractionated carbon beam irradiation. It becomes necessary to construct models that extend the LQ model of conventional radiotherapy for the carbon beam therapy. By combining both Potentially Lethal Damage Repair (PLDR) and Sublethal Damage Repair (SLDR) a new LQ model can develop that aptly modeled the cellular response to fractionated irradiation.