• Journal of Mechanical Science and Technology
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• v.15 no.7
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• pp.876-888
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• 2001

For a large scaled optimization based on response surface methods, an efficient quadratic approximation method is presented in the context of the trust region model management strategy. If the number of design variables is η, the proposed method requires only 2η+1 design points for one approximation, which are a center point and tow additional axial points within a systematically adjusted trust region. These design points are used to uniquely determine the main effect terms such as the linear and quadratic regression coefficients. A quasi-Newton formula then uses these linear and quadratic coefficients to progressively update the two-factor interaction effect terms as the sequential approximate optimization progresses. In order to show the numerical performance of the proposed method, a typical unconstrained optimization problem and two dynamic response optimization problems with multiple objective are solved. Finally, their optimization results compared with those of the central composite designs (CCD) or the over-determined D-optimality criterion show that the proposed method gives more efficient results than others.

• Journal of Integrative Natural Science
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• v.9 no.1
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• pp.10-15
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• 2016

In this paper the approximation methods of offset curve of conic with explicit error bound are considered. The quadratic approximation of conic(QAC) method, the method based on quadratic circle approximation(BQC) and the Pythagorean hodograph cubic(PHC) approximation have the explicit error bound for approximation of offset curve of conic. We present the explicit upper bound of the Hausdorff distance between the offset curve of conic and its PHC approximation. Also we show that the PHC approximation of any symmetric conic is closer to the line passing through both endpoints of the conic than the QAC.

• The Korean Journal of Applied Statistics
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• v.29 no.4
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• pp.571-579
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• 2016

Most of studies related to the distributions of quadratic forms are conducted under the assumption of multivariate normal distribution. In this paper, we suggested an approximation to the distribution of quadratic forms based on multivariate skew-normal distribution as alternatives for multivariate normal distribution. Saddlepoint approximations are considered and the accuracy of the approximations are verified through simulation studies.

• Communications of the Korean Mathematical Society
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• v.31 no.4
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• pp.819-825
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• 2016

In this paper, we establish approximation of bi-quadratic functional equations in Lipschitz spaces.

• Journal of Integrative Natural Science
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• v.7 no.2
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• pp.124-129
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• 2014

In this paper, we construct an logarithmic spiral-like curve using curvature-continuous quadratic spline and quadratic rational spline. The quadratic (rational) spline has self-similarity. We present some properties of the quadratic spline. Also using this $G^2$ quadratic spline, an approximation of logarithmic spiral is proposed and error analysis is obtained.

• Journal of Mechanical Science and Technology
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• v.15 no.9
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• pp.1257-1267
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• 2001

For efficient mechanical system optimization, a new two-point approximation method is presented. Unlike the conventional two-point approximation methods such as TPEA, TANA, TANA-1, TANA-2 and TANA-3, this introduces the shifting level into each exponential intervening variable to avoid the lack of definition of the conventional exponential intervening variables due to zero-or negative-valued design variables. Then a new quadratic approximation whose Hessian matrix has only diagonal elements of different values is proposed in terms of these shifted exponential intervening variables. These diagonal elements are determined in a closed form that corrects the typical error in the approximate gradient of the TANA series due to the lack of definition of exponential type intervening variables and their incomplete second-order terms. Also, a correction coefficient is multiplied to the pre-determined quadratic term to match the value of approximate function with that of the previous point. Finally, in order to show the numerical performance of the proposed method, a sequential approximate optimizer is developed and applied to solve six typical design problems. These optimization results are compared with those of TANA-3. These comparisons show that the proposed method gives more efficient and reliable results than TANA-3.

• Journal of applied mathematics & informatics
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• v.12 no.1_2
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• pp.155-164
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• 2003

A method is proposed to predict the distances between given residue pairs (between C$\sub$${\alpha}$/ atoms) of a protein using a sequence to structure mapping by indefinite quadratic approximation. The prediction technique requires a data fitting in three dimensional space with coordinates of the residues of known structured proteins and leads to a numerical ref resentation of 20 amino acids by minimizing a large least norm iteratively. These approximations are used in distance prediction for given residue pairs. Some computational experience on a test set of small proteins from Brookhaven Protein Data Bank are given.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.21 no.8
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• pp.1218-1228
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• 1997

The move limit strategy is used to avoid the excessive approximation in the structural optimization. The size of move limit has been obtained by engineering experience. Recently, efforts based on analytic methods are performed by some researchers. These methods still have problems, such as prematurity or oscillation of the move limit size. The existing methods usually control the bound of design variables based on the magnitude. Thus, they can not properly handle the configuration variables based on the geometry in the configuration optimization. In this research, the size of move limit is calculated based on the accuracy of approximation. The method is coded and applied to the two-point reciprocal quadratic approximation method. The efficiency is evaluated through examples.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.12
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• pp.2483-2491
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• 2002

This study presents an efficient method for robust optimal design. In order to avoid the excessive evaluations of the exact performance functions, two-point diagonal quadratic approximation method is employed for approximating them during optimization process. This approximation method is one of the two point approximation methods. Therefore, the second order sensitivity information of the approximated performance functions are calculated by an analytical method. As a result, this enables one to avoid the expensive evaluations of the exact $2^{nd}$ derivatives of the performance functions unlike the conventional robust optimal design methods based on the gradient information. Finally, in order to show the numerical performance of the proposed method, one mathematical problem and two mechanical design problems are solved and their results are compared with those of the conventional methods.

• Proceedings of the KSME Conference
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• 2001.06c
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• pp.386-391
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• 2001

This paper presents a new two-point approximation method based on the exponential intervening variable. To avoid the lack of definition of the conventional exponential intervening variables due to zero- or negative-valued design variables the shifting level into each exponential intervening variable is introduced. Then a new quadratic approximation, whose Hessian matrix has only diagonal elements of different values, is proposed in terms of these intervening variables. These diagonal elements are computed in a closed form, which correct the typical error in the approximate gradient of the TANA series due to the lack of definition of exponential type intervening variables and their incomplete second-order terms. Also, a correction coefficient is multiplied to the pre-determined quadratic term to match the value of approximate function with that of the original function at the previous point. Finally, the authors developed a sequential approximate optimizer, solved several typical design problems used in the literature and compared these optimization results with those of TANA-3. These comparisons show that the proposed method gives more efficient and reliable results than TANA-3.