• Title/Summary/Keyword: Newton′s method

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An unwanted facility location problem with negative influence cost and transportation cost (기피비용과 수송비용을 고려한 기피시설 입지문제)

  • Yang, Byoung-Hak
    • Journal of the Korea Safety Management & Science
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    • v.15 no.1
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    • pp.77-85
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    • 2013
  • In the location science, environmental effect becomes a new main consideration for site selection. For the unwanted facility location selection, decision makers should consider the cost of resolving the environmental conflict. We introduced the negative influence cost for the facility which was inversely proportional to distance between the facility and residents. An unwanted facility location problem was suggested to minimize the sum of the negative influence cost and the transportation cost. The objective cost function was analyzed as nonlinear type and was neither convex nor concave. Three GRASP (Greedy Randomized adaptive Search Procedure) methods as like Random_GRASP, Epsilon_GRASP and GRID_GRASP were developed to solve the unwanted facility location problem. The Newton's method for nonlinear optimization problem was used for local search in GRASP. Experimental results showed that quality of solution of the GRID_GRASP was better than those of Random_GRASP and Epsilon_GRASP. The calculation time of Random_GRASP and Epsilon_GRASP were faster than that of Grid_GRASP.

Computer Simulation of the Computational Method in Fuel Optimal Control

  • Lee, B.J.
    • Nuclear Engineering and Technology
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    • v.4 no.1
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    • pp.11-22
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    • 1972
  • Determination of a two-point boundary value problem is the key of finding the control function u(t) with the application of the fundamental idea of Minimum principle. The late development shows the discovery of the initial costate vector for the solution of a two-point value problem. As a new technique of determining the optimal control function, Newton's Sequential method is examined about a number of engineering problems and found available.

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Computational Method of Fuel Optimal Control in Regulator System

  • Lee, Bong-Jin
    • Nuclear Engineering and Technology
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    • v.1 no.2
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    • pp.79-85
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    • 1969
  • Determination of a two-point boundary value problem is the key of finding the control function u(f) with the application of the fundamental idea of Minimum principle. The late development shows the discovery of the initial testate vector for the solution of a two-point value problem. As a new technique of determining the optimal control function, Newton's sequential method is examined in this paper.

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Load Flow Calculation Using Genetic Algorithm (유전자 알고리듬을 이용한 조류계산)

  • Kim, H.;Lee, J.;Cha, J.;Choi, J.;Kwon, S.
    • Proceedings of the KIEE Conference
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    • 2005.07a
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    • pp.78-80
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    • 2005
  • The load flow calculation is one of the most critical issues in electrical power systems. Generally, load flow has been calculated by Gauss-Seidel method and Newton-Raphson method but these methods have some problems such as non-convergence due to heavy load and initial value. In this paper, to overcome such problems, the power flow is calculated by genetic algorithm. At the heavy load, the solution for problem can not be obtained by the Newton-Raphson method. However, it can be solved in case of using genetic algorithm. In this paper, the strong point of this method would be demonstrated in application to an example system.

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Fixed-point Iteration for the Plastic Deformation Analysis of Anisotropic Materials (이방성 재료의 소성변형 해석을 위한 고정점 축차)

  • Seung-Yong Yang;Jeoung Han Kim
    • Journal of Powder Materials
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    • v.30 no.1
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    • pp.29-34
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    • 2023
  • A fixed-point iteration is proposed to integrate the stress and state variables in the incremental analysis of plastic deformation. The Conventional Newton-Raphson method requires a second-order derivative of the yield function to generate a complicated code, and the convergence cannot be guaranteed beforehand. The proposed fixed-point iteration does not require a second-order derivative of the yield function, and convergence is ensured for a given strain increment. The fixed-point iteration is easier to implement, and the computational time is shortened compared with the Newton-Raphson method. The plane-stress condition is considered for the biaxial loading conditions to confirm the convergence of the fixed-point iteration. 3-dimensional tensile specimen is considered to compare the computational times in the ABAQUS/explicit finite element analysis.

Statistical Modeling of Learning Curves with Binary Response Data (이항 반응 자료에 대한 학습곡선의 모형화)

  • Lee, Seul-Ji;Park, Man-Sik
    • Communications for Statistical Applications and Methods
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    • v.19 no.3
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    • pp.433-450
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    • 2012
  • As a worker performs a certain operation repeatedly, he tends to become familiar with the job and complete it in a very short time. That means that the efficiency is improved due to his accumulated knowledge, experience and skill in regards to the operation. Investing time in an output is reduced by repeating any operation. This phenomenon is referred to as the learning curve effect. A learning curve is a graphical representation of the changing rate of learning. According to previous literature, learning curve effects are determined by subjective pre-assigned factors. In this study, we propose a new statistical model to clarify the learning curve effect by means of a basic cumulative distribution function. This work mainly focuses on the statistical modeling of binary data. We employ the Newton-Raphson method for the estimation and Delta method for the construction of confidence intervals. We also perform a real data analysis.

Two-Dimensional Simulation of MOS Transistors Using Numerical Method (수치해석 방법에 의한 2차원적인 MOS Transistor의 시뮬레이션에 관한 연구)

  • 정태성;경종민
    • Journal of the Korean Institute of Telematics and Electronics
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    • v.22 no.5
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    • pp.93-101
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    • 1985
  • A two-dimensional numerical analysis progranl, called SOMOS ( simulation of MO5 transistors), has been developed for the simulation of MOSFET's with various channel lengths and bias conditions. The finite difference approximation of the fundamental equa-tions are formulated using Newton's method for Poisson's equation and the divergence theorem for the continuity equation. For the solution of the lincariBed equations, SOR (successive over relaxation) method and Gummel's algorithm have been employed, The total simulation time for oar operating point is varying between 30 sec. and 4 min. on VAX 11/780 depending on bias conditions, The nonuniform mesh was generated and refined automatically to account for various bias values and the potential distributions.

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ADAPTATION OF THE MINORANT FUNCTION FOR LINEAR PROGRAMMING

  • Leulmi, S.;Leulmi, A.
    • East Asian mathematical journal
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    • v.35 no.5
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    • pp.597-612
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    • 2019
  • In this study, we propose a new logarithmic barrier approach to solve linear programming problem using the projective method of Karmarkar. We are interested in computation of the direction by Newton's method and of the step-size using minorant functions instead of line search methods in order to reduce the computation cost. Our new approach is even more beneficial than classical line search methods. We reinforce our purpose by many interesting numerical simulations proved the effectiveness of the algorithm developed in this work.

Influence Analysis of the Common Mean Problem

  • Kim, Myung Geun
    • Communications for Statistical Applications and Methods
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    • v.20 no.3
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    • pp.217-223
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    • 2013
  • Two influence diagnostic methods for the common mean model are proposed. First, an investigation of the influence of observations according to minor perturbations of the common mean model is made by adapting the local influence method which is based on the likelihood displacement. It is well known that the maximum likelihood estimates are in general sensitive to influential observations. Case-deletions can be a candidate for detecting influential observations. However, the maximum likelihood estimators are iteratively computed and therefore case-deletions involve an enormous amount of computations. An approximation by Newton's method to the maximum likelihood estimator obtained after a single observation was deleted can reduce much of computational burden, which will be treated in this work. A numerical example is given for illustration and it shows that the proposed diagnostic methods can be useful tools.

Analysis on the flow of $U_3O_8$ powder for design of the voloxidizer (건식분말화 장치설계를 위한 $U_3O_8$ 분말의 미세입자 유동해석)

  • Kim Y. H.;Jung J. H.;Hong D. H.;Yoon J. S.
    • Proceedings of the Korean Society for Technology of Plasticity Conference
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    • 2005.05a
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    • pp.454-457
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    • 2005
  • Voloxidizer for hot cell demonstration that handle spend fuel of high radiation virulence in limited space should become a small size and not scatter in its exit. This study determine optimum velocity of $U_3O_8$ using Newton-Raphson Method. We have conducted fortran programing on the Newton-Raphson Method, obtained a theory results and, predicted optimum velocity on the particle size distribution of $U_3O_8$. We have conducted experimentation using acrylic experimental device for verification of theory method, sampled and analyzed using the particle size analyzer In the results, we have found maximum $5\~7\%$ error rate in the comparative value of theory and experimentation. Optimum velocity and experimental results of $U_3O_8$ for scatter prevention have applied for design of demonstration voloxidizer, and produced operation condition of voloxidizer.

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