• Journal of applied mathematics & informatics
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• 제20권1_2호
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• pp.239-254
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• 2006

An efficient descent method for unconstrained optimization problems is line search method in which the step size is required to choose at each iteration after a descent direction is determined. There are many ways to choose the step sizes, such as the exact line search, Armijo line search, Goldstein line search, and Wolfe line search, etc. In this paper we propose a new inexact line search for a general descent method and establish some global convergence properties. This new line search has many advantages comparing with other similar inexact line searches. Moreover, we analyze the global convergence and local convergence rate of some special descent methods with the new line search. Preliminary numerical results show that the new line search is available and efficient in practical computation.

• Journal of applied mathematics & informatics
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• 제27권1_2호
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• pp.233-243
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• 2009

This paper concerns an algorithm that combines line search and trust region step for nonlinear optimization problems. Unlike traditional trust region methods, we incorporate the Armijo line search technique into trust region method to solve the subproblem. In addition, the subproblem is solved accurately, but instead solved by inaccurate method. If a trial step is not accepted, our algorithm performs the Armijo line search from the failed point to find a suitable steplength. At each iteration, the subproblem is solved only one time. In contrast to interior methods, the optimal solution is derived by iterating from outside of the feasible region. In numerical experiment, we apply the algorithm to nonlinear portfolio optimization problems, primary numerical results are presented.

• 충청수학회지
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• 제21권1호
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• pp.117-127
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• 2008

The performance of a modified Armijo line search rule related to BFGS gradient type method with the results from other well-known line search rules are compared as well as analyzed. Although the modified Armijo rule does require as much computational cost as the other rules, it shows more efficient in finding local minima of unconstrained optimization problems. The sensitivity of the parameters used in the line search rules is also analyzed. The results obtained by implementing algorithms in Matlab for the test problems in [3] are presented.

• Journal of applied mathematics & informatics
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• 제29권5_6호
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• pp.1303-1309
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• 2011

Based on the PRP method, a new spectral PRP conjugate gradient method has been proposed to solve general unconstrained optimization problems which produce sufficient descent search direction at every iteration without any line search. Under the Wolfe line search, we prove the global convergence of the new method for general nonconvex functions. The numerical results show that the new method is efficient for the given test problems.

• 대한전자공학회논문지SP
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• 제43권4호
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• pp.55-65
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• 2006

대부분의 고속 블록 움직임 추정 알고리즘은 탐색점의 수를 줄여서 연산량을 감소시킨다. 하지만 이러한 고속 움직임 추정 알고리즘들은 비정규화 데이터 흐름 때문에 멀티미디어 프로세서에서는 좋은 성능을 보이기 어렵다. 미디어 프로세서에서는 내부 메모리에서 데이터의 효과적인 재사용이 SAD 명령의 수를 줄이는 것보다 더욱 중요하다. 이는 수행 사이클의 성능이 외부 메모리 액세스의 횟수에 매우 의존적이기 때문이다. 따라서 본 논문에서는 내부 메모리로부터 데이터를 효과적으로 재사용 할 수 있는 라인 탐색 패턴과 라인 탐색 패턴에서 불필요한 SAD 연산을 줄이기 위한 서브 샘플링 방법을 적용한 Hexagon 모양 라인 탐색(Hexagon-shape line search, HEXSLS) 기법을 제안한다. 모의실험을 통하여 HEXSLS 기법의 MAE 성능은 전역 탐색 블록 정합(FSBMA) 기법과 비슷하고, Hexagon 기반 탐색 (Hexagon-based search) 보다 우수한 성능을 가짐을 보인다. 또한 HEXSLS는 Hexagon 기반 탐색이나 예측 라인 탐색(predictive line search) 기법보다 적은 외부 메모리의 액세스가 발생한다. 결과적으로, 제안한 HEXSLS 기법은 종래의 기법과 비교하여 미디어 프로세서에서 매우 낮은 수행 사이클 성능을 보인다.

• Journal of applied mathematics & informatics
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• 제34권1_2호
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• pp.157-165
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• 2016

In this paper, we develop a new hybridization conjugate gradient method for solving the unconstrained optimization problem. Under mild assumptions, we get the sufficient descent property of the given method. The global convergence of the given method is also presented under the Wolfe-type line search and the general Wolfe line search. The numerical results show that the method is also efficient.

• Journal of applied mathematics & informatics
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• 제31권3_4호
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• pp.373-378
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• 2013

In this paper, we consider two kinds of the Levenberg-Marquardt method for solve a system of nonlinear equations. We use line search on every iteration to guarantee that the Levenberg-Marquardt methods are globally convergent. Under mild conditions, we prove that while the de- scent condition can be satisfied at the iteration of the Levenberg-Marquardt method, the global convergence of the method can be established.

• East Asian mathematical journal
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• 제35권5호
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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.

• Journal of applied mathematics & informatics
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• 제14권1_2호
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• pp.123-136
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• 2004

In this paper, a combining trust region and line search algorithm for equality constrained optimization is proposed. At each iteration, we only need to solve the trust region subproblem once, when the trust region trial step can not be accepted, we switch to line search to obtain the next iteration. Hence, the difficulty of repeated solving trust region subproblem in an iterate is avoided. In order to allow the direction of negative curvature, we add second correction step in trust region step and employ nonmonotone technique in line search. The global convergence and local superlinearly rate are established under certain assumptions. Some numerical examples are given to illustrate the efficiency of the proposed algorithm.

• 대한기계학회논문집A
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• 제27권8호
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• pp.1281-1286
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• 2003

A line search algorithm to increase a convergence in Newton's method is developed and applied to nonlinear finite element analysis. The algorithm is based on the slack line search theory which is an efficient algorithm to determine initial acceleration coefficient, variable backtracking algorithm proposed by some researchers, and convergence criterion based on residual norm. Also, it is capable of avoiding exceptional diverging conditions. Developed program is tested in metal forming simulation such as forging and ring rolling. Numerical result shows the validity of the algorithm for a highly nonlinear system .