• Journal of applied mathematics & informatics
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• 제22권1_2호
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• pp.461-466
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• 2006

In this paper, an algorithm with a new Armijo-type line search is proposed that ensure global convergence of a correlative Polak-Ribiere conjugate method for the unconstrained minimization of non-convex differentiable function.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제8권2호
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• pp.7-13
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• 2004

A Conjugate Gradient (CG) algorithm for unconstrained minimization is proposed which is invariant to a nonlinear scaling of a strictly convex quadratic function and which generates mutually conjugate directions for extended quadratic functions. It is derived for inexact line searches and is designed for the minimization of general nonlinear functions. It compares favorably in numerical tests with the original Dixon algorithm on which the new algorithm is based.

• 대한수학회지
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• 제47권6호
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• pp.1253-1267
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• 2010

This paper considers the unconstrained global optimization with the revised filled function methods. The minimization sequence could leave from a local minimizer to a better minimizer of the objective function through minimizing an auxiliary function constructed at the local minimizer. Some promising numerical results are also included.

• Journal of applied mathematics & informatics
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• 제24권1_2호
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• pp.367-376
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• 2007

In this paper we consider the global convergence of a new super memory gradient method for unconstrained optimization problems. New trust region radius is proposed to make the new method converge stably and averagely, and it will be suitable to solve large scale minimization problems. Some global convergence results are obtained under some mild conditions. Numerical results show that this new method is effective and stable in practical computation.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2000년도 하계학술대회 논문집 B
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• pp.744-746
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• 2000

This paper presents an optimum design of a linear induction motor(LIM) using genetic algorithm(GA). Sequential unconstrained minimization technique(SUMT) is used to transform the nonlinear optimization with constraints to a simple unconstrained problem. The objective functions of LIM such as trust, weight are optimized and the result was applied to the design of linear induction pump.

• Journal of applied mathematics & informatics
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• 제23권1_2호
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• pp.311-319
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• 2007

This article studies a modified BFGS algorithm for solving smooth unconstrained strongly convex minimization problem. The modified BFGS method is based on the new quasi-Newton equation $B_k+1{^s}_k=yk\;where\;y_k^*=yk+A_ks_k\;and\;A_k$ is a matrix. Wei, Li and Qi [WLQ] have proven that the average performance of two of those algorithms is better than that of the classical one. In this paper, we prove the global convergence of these algorithms associated to a general line search rule.

• 한국강구조학회 논문집
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• 제16권1호통권68호
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• pp.21-32
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• 2004

본 연구에서는 다제약 설계변수를 갖는 비선형 문제를 무제약 최소화 문제로 전환하는 축차무제약 최소화기법(SUMT)과 효과적인 강골조의 2차비탄성해석 방법 중의 하나인 개선소성힌지해석 방법을 접목시킨 평면 강골조의 연속최적설계 모델 및 프로그램을 개발하였다. 최적설계를 위한 목적함수로는 강골조물을 구성하는 모든 부재의 중량 합을, 제약조건으로는 AISC-LRFD의 휨강도, 전단강도, 압축 및 인장강도, 국부좌굴 및 부재좌굴, 그리고 단면형상 등에 관한 설계기준을 사용하였다. 본 연구에서 개발한 연속최적설계 모델을 이용하여 여러 평면 강골조의 최적설계를 수행하였으며, 최적설계 견과로부터 개발한 연속최적설계 모델의 사용성, 타당성, 효율성 및 경제성 등을 검토하였다.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제9권1호
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• pp.55-61
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• 2005

A Conjugate Gradient algorithm for unconstrained minimization is proposed which is invariant to a nonlinear scaling of a strictly convex quadratic function and which generates mutually conjugate directions for extended quadratic functions. It is derived for inexact line searches and for general functions. It compares favourably in numerical tests (over eight test functions and dimensionality up to 1000) with the Dixon (1975) algorithm on which this new algorithm is based.

• Journal of applied mathematics & informatics
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• 제24권1_2호
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• pp.325-331
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• 2007

To the unconstrained programme of non-convex function, this article give a modified BFGS algorithm associated with the general line search model. The idea of the algorithm is to modify the approximate Hessian matrix for obtaining the descent direction and guaranteeing the efficacious of the new quasi-Newton iteration equation $B_{k+1}s_k=y^*_k,\;where\;y^*_k$ is the sum of $y_k\;and\;A_ks_k,\;and\;A_k$ is some matrix. The global convergence properties of the algorithm associating with the general form of line search is proved.

• 오토저널
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• 제4권2호
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• pp.79-85
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• 1982

Computer codes on two numerical optimization methods-Sequentially Unconstrained Minimization Technique (SUMT) and Gradient Projection Method-are constructed and tested with several test problems. Design formulation of tension - compression coil spring is set up and the solution is obtained. Consequently, the feature, the advantage and the limitation of these methods, made clear through the tests, are discussed.