• Journal of Korean Society of Transportation
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• v.6 no.1
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• pp.5-16
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• 1988

Development is given to an optimal network design method using continuous design variables. Modified Hooke-and-Jeeves algorithm is implemented in order to solve nonlinear programming problem which is approximately equivalent to the real network design problem with system efficiency crieteria and improvement cost as objective function. the method was tested for various forms of initial solution, and dimensions of initial step size of link improvements. At each searching point of evaluating the objective function, a link flow problem was solved with user equilibrium principles using the Frank-Wolfe algorithm. The results obtained are quite promising interms fo numbers of evaluation, and the speed of convergence. Suggestions are given to selections of efficient initial solution, initial step size and convergence criteria. An approximate method is also suggested for reducing computation time.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.5 no.2
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• pp.25-37
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• 2001

We consider the finite element method applied to nonlinear Sobolev equation with smooth data and demonstrate for arbitrary order ($k{\geq}2$) finite element spaces the optimal rate of convergence in $L_{\infty}\;W^{1,{\infty}}({\Omega})$ and $L_{\infty}(L_{\infty}({\Omega}))$ (quasi-optimal for k = 1). In other words, the nonlinear Sobolev equation can be approximated equally well as its linear counterpart. Furthermore, we also obtain superconvergence results in $L_{\infty}(W^{1,{\infty}}({\Omega}))$ for the difference between the approximate solution and the generalized elliptic projection of the exact solution.

• Journal of the Korean Society for Precision Engineering
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• v.11 no.1
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• pp.166-176
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• 1994

The problem of reducing the vibration level of elastic plates driven by multiple random point forces is analyzed in this study. First, the analytical solution for the vibration level of finite thin plates with four simply supported edges under the action of multiple random point force is derived. By assuming the plates to be lightly damped, an approximate solution for the vibration level of the plate is obtained. A numerical study is carried out to determine an optimal spacing distance between the multiple point forces in order to produce a relative minimum in the plate's vibration level. The optimal spacing distance is shown to depend on the given excitation band. The effects of wave cancellation in the near field of the multiple point forces are discussed by using the equivalence of certain stationary random responses and deterministic pulse responese.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.231-244
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• 2007

In this paper, we use measure theory for considering asymptotically stable of an autonomous system [1] of first order nonlinear ordinary differential equations(ODE's). First, we define a nonlinear infinite-horizon optimal control problem related to the ODE. Then, by a suitable change of variable, we transform the problem to a finite-horizon nonlinear optimal control problem. Then, the problem is modified into one consisting of the minimization of a linear functional over a set of positive Radon measures. The optimal measure is approximated by a finite combination of atomic measures and the problem converted to a finite-dimensional linear programming problem. The solution to this linear programming problem is used to find a piecewise-constant control, and by using the approximated control signals, we obtain the approximate trajectories and the error functional related to it. Finally the approximated trajectories and error functional is used to for considering asymptotically stable of the original problem.

• Journal of applied mathematics & informatics
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• v.30 no.5_6
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• pp.719-728
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• 2012

In this paper, we develop a numerical method to solving an optimal control problem, which is governed by a parabolic partial differential equations(PDEs). Our approach is to approximate the PDE problem to initial value problem(IVP) in $\mathbb{R}$. Then, the homogeneous part of IVP is solved using semigroup theory. In the next step, the convergence of this approach is verified by properties of one-parameter semigroup theory. In the rest of paper, the original optimal control problem is solved by utilizing the solution of homogeneous part. Finally one numerical example is given.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.399-409
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• 2007

In this paper we use iterative dynamic programming in the discrete case to solve a wide range of the nonlinear equations systems. First, by defining an error function, we transform the problem to an optimal control problem in discrete case. In using iterative dynamic programming to solve optimal control problems up to now, we have broken up the problem into a number of stages and assumed that the performance index could always be expressed explicitly in terms of the state variables at the last stage. This provided a scheme where we could proceed backwards in a systematic way, carrying out optimization at each stage. Suppose that the performance index can not be expressed in terms of the variables at the last stage only. In other words, suppose the performance index is also a function of controls and variables at the other stages. Then we have a nonseparable optimal control problem. Furthermore, we obtain the path from the initial point up to the approximate solution.

• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.29-51
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• 2004

In this paper, we propose a new mixed finite element method, called the characteristics-mixed method, for approximating the solution to Burgers' equation. This method is based upon a space-time variational form of Burgers' equation. The hyperbolic part of the equation is approximated along the characteristics in time and the diffusion part is approximated by a mixed finite element method of lowest order. The scheme is locally conservative since fluid is transported along the approximate characteristics on the discrete level and the test function can be piecewise constant. Our analysis show the new method approximate the scalar unknown and the vector flux optimally and simultaneously. We also show this scheme has much smaller time-truncation errors than those of standard methods. Numerical example is presented to show that the new scheme is easily implemented, shocks and boundary layers are handled with almost no oscillations. One of the contributions of the paper is to show how the optimal error estimates in $L^2(\Omega)$ are obtained which are much more difficult than in the standard finite element methods. These results seem to be new in the literature of finite element methods.

• Journal of Korean Society for Quality Management
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• v.14 no.1
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• pp.33-38
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• 1986

This paper deals with probabilistic order level inventory system which the quantity ordered at the end of the scheduling period is dependent on lead times. To find an optimal solution, pearson system of distributions is used to approximate the probability density function of the on-order quantity. An example is solved and sensitivity analysis is performed to examine the relation between lead times and the ordering quantity.

• 전기의세계
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• v.29 no.4
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• pp.256-259
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• 1980

A singular pertubation theory is applied to obtain an approximate solution for suboptimal control of nuclear reactors with spatially distributed parameters. The inverse of the neutron velocity is regarded as a small perturbing parameter, and the model, adopted for simplicity, is a cylindrically symmetrical reactor whose dynamics are described by the one group diffusion equation with one delayed neutron group. The Helmholtz mode expansion is used for the application of the optimal theory for lumped parameter systems to the spatially distributed parameter systems. An asymptotic expansion of the feedback gain matrix is obtained with construction of the boundary layer correction up to the first order.

• Korean Journal of Computational Design and Engineering
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• v.1 no.2
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• pp.107-121
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• 1996

An optimization procedure is proposed to determine the optimal stacking sequence on the buckling of laminated composite plates with midplane symmetry under various loading conditions. Classical lamination theory is used for the determination of the critical buckling load of simply supported angle-ply laminates. Analysis is performed by the Galerkin method and Rayleigh-Ritz method. The approximate solution of buckling is replaced by the algorithms that produce generalized eigenvalue problem. Direct search technique is employed to solve the optimization problem effectively. A series of computations is carried out for plates having different aspect ratios, different load ratios and different number of lay-ups.