• Journal of the korean Society of Automotive Engineers
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• v.11 no.2
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• pp.24-33
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• 1989

본 고에서는 이러한 추세에 따라서, 보다 효율적인 optimization program에 대해서 소개하고자 한다. 사용한 최적화 알고리즘은 ALM(augmented lagrange multiplier) 방법을 적용해서 구속조건이 있는 문제를 구속조건이 없는 문제로 변환한 후, self-scaling BFGS(broydon-flecher-goldfarb-schanno)를 적용한다. BFGS의 각 descent 방향에서의 step 길이는, sequential search로 unimodal point를 구해서, golden section 방법으로 refine을 한후, cubic approximation을 적용해서 구한다.

• Water for future
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• v.29 no.3
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• pp.177-186
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• 1996

QUAL2E model was applied to assess the water quality variations due to dredging of the bottom deposit in the downstream of the Nakdong River. A variedflow analysis was performed for the reach of Namji to Nakdong Estuary to estimate the hydraulic parameters. BFGS (Broyden-Fletcher-Goldfarb-Shanno) method was applied to determine the optimum reaction parameters and model verrification was performed based on these. Water quality modeling of dredging effects for BOD and DO in the reach was performed under low and average flow conditions and alternatives. It revealed that dredging had significant effedcts on the improvement of water quality in the reach.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.6 no.1
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• pp.91-107
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• 2002

This paper presents two new self-scaling variable-metric algorithms. The first is based on a known two-parameter family of rank-two updating formulae, the second employs an initial scaling of the estimated inverse Hessian which modifies the first self-scaling algorithm. The algorithms are compared with similar published algorithms, notably those due to Oren, Shanno and Phua, Biggs and with BFGS (the best known quasi-Newton method). The best of these new and published algorithms are also modified to employ inexact line searches with marginal effect. The new algorithms are superior, especially as the problem dimension increases.

• Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
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• 2000.11a
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• pp.363-371
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• 2000

There are some concepts that could achieve Near-Field Recording (NPR). One of concepts is the use of the flying head with Solid Immersion Lens (SIL). The basic concept of this is almost same with that of Hard Disk Drive (HDD). This study presents the flying characteristics of the slider for NFR. Numerical simulations are performed using FEM and Broydon-Fletcher-Goldfarb-Shanno (BFGS) method. Some modifications are considered to improve flying characteristics of the slider.

• Journal of Korea Water Resources Association
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• v.35 no.4 s.129
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• pp.385-395
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• 2002

A stochastic model using FOEA(First-Order Error-Analysis) and Monte Carlo Method is developed to predict water quality variation in a river. A sensitivity analysis using influential matrix is performed to determine the significant reaction coefficients. Also the BFGS (Broyden-Fletcher-Goldfarb-Shanno) optimization method is applied to estimate the optimal values of the major reaction coefficients. The developed stochastic model is applied to the real study reach and the results are agreed well with those of deterministic analysis. The process for analyzing the uncertainties of the discharge, water quality and reaction coefficients of headwater and tributaries is included in the model to estimate the influence on the water quality variation at downstream. The extents of contribution of the uncertainties influencing on the total uncertainty can be evaluated from the results of the model.

• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.2
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• pp.544-556
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• 1991

The optimization of many engineering design problems requires a nonlinear programming algorithm that is robust and efficient. A general-purpose nonlinear optimization program IDOL (Interactive Design Optimization Library) is developed based on the Augmented Lagrange Mulitiplier (ALM) method. The ideas of selecting a good initial design point, using resonable initial values for Lagrange multipliers, constraints scaling, descent vector restarting, and dynamic stopping criterion are employed for computational enhancement to the ALM method. A descent vector is determined by using the Broydon-Fletcher-Goldfarb-Shanno (BFGS) method. For line search, the Incremental-Search method is first used to find bounds on the solution, then the bounds are reduced by the Golden Section method, and finally a cubic polynomial approximation technique is applied to locate the next design point. Seven typical test problems are solved to show IDOL efficient and robust.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.24 no.10
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• pp.1335-1342
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• 2000

Three-dimensional flow analysis and numerical optimization methods are presented for the design of an axial-flow fan. Steady, incompressible, three-dimensional Reynolds-averaged Navier-Stokes equations are used as governing equations, and standard k- ${\varepsilon}$ turbulence model is chosen as a turbulence model. Governing equations are discretized using finite volume method. Steepest descent method, conjugate gradient method and BFGS method are compared to determine the searching directions. Golden section method and quadratic fit-sectioning method are tested for one dimensional search. Objective function is defined as a ratio of generation rate of the turbulent kinetic energy to pressure head. Two variables concerning sweep angle distribution are selected as the design variables. Performance of the final fan designed by the optimization was tested experimentally.

• 유체기계공업학회:학술대회논문집
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• 1999.12a
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• pp.221-226
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• 1999

Three-dimensional flow analysis and numerical optimization methods are presented for the design of an axial-flow fan. Steady, Incompressible, three-dimensional Reynolds-averaged Wavier-Stokes equations are used as governing equations, and standard k-$\epsilon$ turbulence model is chosen as a turbulence model. Governing equations are discretized using finite volume method. Steepest descent method, conjugate gradient method and BFGS method are compared to determine the searching directions. Golden section method and quadratic fit-sectioning method are tested for one dimensional search. Objective function is defined as a ratio of generation rate of the turbulent kinetic energy to pressure head. Sweep angle distributions are used as design variables.

• Bulletin of the Korean Chemical Society
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• v.15 no.11
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• pp.953-957
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• 1994

Pseudospectral Hartree-Fock(PSHF) gradient calculations with $6-31G^{**}$ basis set have been carried out to determine the structure of D-Asparagine molecule $(C_4N_2O_3H_8)$ with improved grids and with the BFGS method. The modified PSHF method, despite partial optimization of the gradient code, turned out to be still faster than the conventional ab initio method, GAUSSIAN 90 program by more than twice. The optimum geometry of D-Asparagine obtained by the PSHF method is in good agreement with those calculated by the GAUSSIAN 90 program (within 0.0036 ${\AA}$ for bond lengths, 0.8 degrees for bond angles, and 1.6 degrees for torsional angles) except for three torsional angles. Here, rather large discrepancy of these three torsional angles (5-6 degrees) is attributed to the small differences in the optimum bond lengths and angles between the PSHF and GAUSSIAN 90 calculations.

• 한국전산유체공학회:학술대회논문집
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• 2000.10a
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• pp.32-38
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• 2000

Wing flap deflection angles of a supersonic transport are optimized to improve transonic cruise performance. For this end, a numerical optimization method is adopted using a three-dimensional unstructured Euler code and a discrete adjoint code. Deflection angles of ten flaps; five for leading edge and five fur railing edge, are employed as design variables. The elliptic equation method is adopted for the interior grid modification during the design process. Interior grid sensitivities are neglected for efficiency. Also tested is the validity of the approximate gradient evaluation method for the present design problem and found that it is applicable for loading edge flap design in cases of no shock waves on the wing surface. The BFGS method is used to minimize the drag with constraints on the lift and upper surface Mach numbers. Two design examples are conducted; one is leading edge flap design, and the other is simultaneous design of leading edge and trailing edge flaps. The latter gave a smaller drag than the former by about two counts.