• Journal of Mechanical Science and Technology
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• 제15권9호
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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.

• Kyungpook Mathematical Journal
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• 제46권3호
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• pp.389-397
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• 2006

A fixed point theorem of Singh and Singh [10] is generalized to locally convex spaces and the new result is applied to extend a result on invariant approximation of Jungck and Sessa [5].

• 한국수학교육학회지시리즈A:수학교육
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• 제18권1호
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• pp.21-23
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• 1980

In [3], an extension of B. Brosowski s T-invariant Point Theorem is given where the linearity of the function and the convexity of the set are relaxed. In this paper, our main purpose is to generalize S. P. Singh's T-invariant Point Theorem to Approximation Theory.

• 대한수학회보
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• 제44권3호
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• pp.537-545
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• 2007

Necessary conditions for the existence of common fixed points for noncommuting mappings satisfying generalized contractive conditions in the setup of certain metrizable topological vector spaces are obtained. As applications, related results on best approximation are derived. Our results extend, generalize and unify various known results in the literature.

• Journal of Computational Design and Engineering
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• 제3권2호
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• pp.102-111
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• 2016

In this paper, we study the problem of computing smooth feature curves from CAD type point clouds models. The proposed method reconstructs feature curves from the intersections of developable strip pairs which approximate the regions along both sides of the features. The generation of developable surfaces is based on a linear approximation of the given point cloud through a variational shape approximation approach. A line segment sequencing algorithm is proposed for collecting feature line segments into different feature sequences as well as sequential groups of data points. A developable surface approximation procedure is employed to refine incident approximation planes of data points into developable strips. Some experimental results are included to demonstrate the performance of the proposed method.

• Journal of applied mathematics & informatics
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• 제29권3_4호
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• pp.713-719
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• 2011

The problem of approximation from a set of scattered data arises in a wide range of applied mathematics and scientific applications. In this study, we present a quasi-interpolatory approximation scheme for scattered data approximation problem, which reproduces a certain space of polynomials. The proposed scheme is local in the sense that for an evaluation point, the contribution of a data value to the approximating value is decreasing rapidly as the distance between two data points is increasing.

• 대한기계학회논문집A
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• 제35권3호
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• pp.259-266
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• 2011

본 논문에서는 SD-TDQAO (Sequential Dual - Two-point Diagonal Quadratic Approximate Optimization)라는 쌍대기법을 이용한 순차적 최적설계 알고리즘을 제안한다. 이 방법은 비선형 목적함수와 제한조건이 포함되어 있는 공학적인 문제를 효과적으로 풀 수 있도록 하는데 목적이 있다. 기존의 볼록성과 분리성이 만족되지 않는 eTDQA2 방법을 이용하여 쌍대기법에 이용할 수 있도록 이차 근사함수의 헤시언 대각요소에 이를 적용하여 쉽게 볼록성과 분리성을 보장할 수 있도록 하였다. 또한 이를 수학적 예제와 위상 최적설계문제를 통해 기존의 쌍대기법 알고리즘인 MMA 와의 비교로 그 성능을 입증하였다.

• 대한기계학회논문집
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• 제19권2호
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• pp.433-442
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• 1995

For the line search of a multi-variable optimization, an efficient algorithm is presented. The algorithm sequentially employs several polynomial approximations such as 2-point quadratic interpolation, 3-point cubic interpolation/extrapolation and 4-point cubic interpolation/extrapolation. The order of polynomial function is automatically increased for improving the accuracy of approximation. The method of approximation (interpolation or extrapolation) is automatically switched by checking the slope information of the sample points. Also, for selecting the initial step length along the descent vector, a new approach is presented. The performance of the proposed method is examined by solving typical test problems such as mathematical problems, mechanical design problems and dynamic response problems.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2001년도 춘계학술대회논문집C
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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.

• 대한기계학회논문집A
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• 제25권9호
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• pp.1423-1431
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• 2001

Based on the exponential intervening variable, a new two-point approximation method is presented. This introduces the shifting level into each exponential intervening variable to avoid the lack of def inition 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 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.