• Journal of the Korean Data and Information Science Society
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• v.26 no.6
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• pp.1295-1303
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• 2015

In a mixture experiment, one may be interested in estimating not only main effects but also some interactions. Main effects and interactions may be estimated through appropriate designs such as simplex-centroid designs. However, the estimability problems, implied by the sum to one functional relationship among the factors, have strong consequences on the confounding and identifiability of models for such designs. To handle these problems, we address homogeneous polynomial model based on the computational commutative algebra (CCA) instead of using $Scheff{\acute{e}}s$ canonical model which is typically used. The problem posed here is to give how to choose estimable main effects and also some low-degree interactions. The theory is tested using a fraction of simplex-centroid designs aided by a modern computational algebra package CoCoA.

• Proceedings of the Optical Society of Korea Conference
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• 2004.07a
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• pp.244-245
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• 2004

• Proceedings of the KIEE Conference
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• 2006.07d
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• pp.2179-2180
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• 2006

뇌자도 신호원 추정에서, 심플렉스 알고리즘은 비교적 간단하고 도함수가 필요하지 않기 때문에 널리 사용된다. 그러나, 심플렉스 알고리즘은 초기 값에 매우 민감하다. 그래서, 본 논문에서는 효과적으로 초기 값을 선택하는 방법을 제안하였다. 해석영역을 여러 구획으로 나눈 후 각 구획의 중심점에서 목적 함수를 계산하여 가장 좋은 간을 갖는 점을 초기 값으로 정하였다. 선택된 초기 값으로 신호원을 추정하였으며 구획의 수가 증가함에 따른 정확도 향상과 계산 시간을 평가하였다.

• Journal of Industrial Technology
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• v.20 no.B
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• pp.27-34
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• 2000

The definition of flatness is given by ISO, ANSI, KS, etc. but those standards don't mention about the specific methods for the flatness. So various solution models that are based on the Minimum Zone Method have been proposed as an optimization problem for the minimax curve fitting. But it has been rare to compare some optimization algorithms to make a guideline for choosing better algorithms in this field. Hence this paper examined and compared Genetic Algorithm and Simplex Method to the evaluation of flatness. As a result, Genetic Algorithm gave the better or equal flatness than Simplex Method but it has the inefficiency caused from the large number of iteration. Therefore, in the future, another researches about alternative algorithms including Hybrid Genetic Algorithm should be achieved to improve the efficiency of Genetic Algorithm for the evaluation of flatness.

• 한국데이터정보과학회:학술대회논문집
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• 2004.04a
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• pp.111-119
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• 2004

유사이항분포와 유사다항분포를 소개하고 베타분포와 Dirichlet 분포와의 관계를 밝힘으로써 심플렉스상에서 정의되는 성분데이터의 분석을 위한 새로운 방법을 제시하는 토대를 마련하고자 한다.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.12 no.1
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• pp.59-70
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• 1992

Quadratic programming problems(QP) have been widely used as a direction-finding subproblem in the engineering and structural design optimization. To develop an efficient solution algorithm for the QP subproblems, theoretical aspects and numerical behavior of mathematical programming methods that can be used as QP solver are studied and compared. For the solution of both primal and dual QP, Simplex, gradient projection(GRP), and augmented Lagrange multiplier algorithms are investigated and coded. From the numerical study, it is found that the primal GRP algorithm with potential constraint strategy and the dual Simplex algorithm are more attractive and effective than the others. They have theoretical robustness as well. Moreover, primal GRP algorithm is preferable in case the number of constraints is larger than the number of design variables. Favorable features of GRP and Simplex algorithm are merged into a combined algorithm, which is useful in the structural design optimization.

• Journal of Industrial Technology
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• v.22 no.B
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• pp.35-44
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• 2002

To find the optimal solution as rapidly and exactly as possible with Nelder-Mead simplex algorithm, the present values of the reflection, expansion, contraction and/or shrink parameters of this algorithm are needed to be changed at appropriate time during the search process. The reflection parameter is selected in this study in order to be changed because reflection, expansion and contraction process can be simultaneously effected by only this parameter. Two independent indices for determining whether the present value of the reflection parameter of this algorithm should be changed or not during the search process are suggested in this study. Those indices were made of the equations of Nelder-Mead simplex algorithm's convergence criterion and Dennis-Wood's convergence criterion, respectively. It is appeared that the optimal solution can be find with smaller numbers of objective function evaluation than the original Nelder-Mead's one with fixed parameter when the those indices are used during the search process. and the more remarkable reduction effect of the number of an objective function evaluation can be obtained when the latter index is used.

• Journal of Korea Multimedia Society
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• v.7 no.11
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• pp.1531-1539
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• 2004

In this paper, we propose an efficient method for locating human lips. Based on Point Distribution Model and Principle Component Analysis, a lip shape model is built. Lip boundary model is represented based on the concatenated gray level distribution model. We calculate the distribution of shape parameters using Gaussian mixture. The problem to locate lip is simplified as the minimization problem of matching object function. The Down Hill Simplex Algorithm is used for the minimization with Gaussian Mixture for setting initial condition and refining estimate of lip shape parameter, which can refrain iteration from converging to local minima. The experiments have been performed for many images, and show very encouraging result.

• Journal of KIISE:Computer Systems and Theory
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• v.32 no.3
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• pp.133-147
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• 2005

Various types of ray-tracing methods are used to predict the quantity measures of radiation illumination, the uniformity of illumination, radiation performance of LCD BLU(Hack-Light Unit). The uniformity of radiation illumination is one of the most important design factor of BLU and is usually controlled by the diffusive-ink pattern printed on the bottom of light-guide panel of BLU. Therefore it is desirable to produce an improved (ideally, the optimal) ink pattern to achieve the best uniformity of radiation illumination. In this paper, we applied the Welder-Mead simplex-search method among various direct search method to compute the optimal ink pattern. Direct search methods are widely used to optimize the functions which are often highly nonlinear, unpredictably discontinuous, and nondifferentiable, The ink-pattern controlling the uniformity of radiation illumination is one type of these functions. In this paper, we found that simplex search methods are well suited to computing the optimal diffusive-ink pattern. In extensive numerical testing, we have found the simplex search method to be reasonably efficient and reliable at computing the optimal diffusive-ink pattern. The result also suggests that optimization can improve the functionality of simulation tools which are used to design LCD BLU.

• Journal of the military operations research society of Korea
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• v.11 no.1
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• pp.79-86
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• 1985

A multi-interchange simplex method is presented. This method tries to cut almost half of the set of convex combinations which generate all decreasing feasible directions. Analysis of this method indicates high possibility of the existence of polynomial-time simplex-type methods.