• Journal of Mechanical Science and Technology
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• v.15 no.7
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• pp.876-888
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• 2001

For a large scaled optimization based on response surface methods, an efficient quadratic approximation method is presented in the context of the trust region model management strategy. If the number of design variables is η, the proposed method requires only 2η+1 design points for one approximation, which are a center point and tow additional axial points within a systematically adjusted trust region. These design points are used to uniquely determine the main effect terms such as the linear and quadratic regression coefficients. A quasi-Newton formula then uses these linear and quadratic coefficients to progressively update the two-factor interaction effect terms as the sequential approximate optimization progresses. In order to show the numerical performance of the proposed method, a typical unconstrained optimization problem and two dynamic response optimization problems with multiple objective are solved. Finally, their optimization results compared with those of the central composite designs (CCD) or the over-determined D-optimality criterion show that the proposed method gives more efficient results than others.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.12
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• pp.3040-3052
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• 2000

For effective construction of second-order response surface models, an efficient quad ratic approximation method is proposed in the context of trust region model management strategy. In the proposed method, although only the linear and quadratic terms are uniquely determined using 2n+1 design points, the two-factor interaction terms are mathematically updated by normalized quasi-Newton formula. In order to show the numerical performance of the proposed approximation method, a sequential approximate optimizer is developed and solves a typical unconstrained optimization problem having 2, 6, 10, 15, 30 and 50 design variables, a gear reducer system design problem and two dynamic response optimization problems with multiple objectives, five objectives for one and two objectives for the other. Finally, their optimization results are compared with those of the CCD or the 50% over-determined D-optimal design combined with the same trust region sequential approximate optimizer. These comparisons show that the proposed method gives more efficient than others.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.29 no.9 s.240
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• pp.1199-1208
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• 2005

Nowadays, it is performed actively to optimize by using an approximate model. This is called the approximate optimization. In addition, the sequential approximate optimization (SAO) is the repetitive method to find an optimum by considering the convergence of an approximate optimum. In some recent studies, it is proposed to increase the fidelity of approximate models by applying the sequential sampling. However, because the accuracy and efficiency of an approximate model is directly connected with the design area and the termination criteria are not clear, sequential sampling method has the disadvantages that could support an unreasonable approximate optimum. In this study, the SAO is executed by using trust region, Kriging model and Optimal Latin Hypercube design (OLHD). Trust region is used to guarantee the convergence and Kriging model and OLHD are suitable for computer experiment. finally, this SAO method is applied to various optimization problems of highly nonlinear mathematical functions. As a result, each approximate optimum is acquired and the accuracy and efficiency of this method is verified by comparing with the result by established method.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.29 no.6 s.237
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• pp.842-851
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• 2005

In this paper, a new method for constrained optimization of noisy functions is proposed. In approximate optimization using response surface methods, if constraints have severe noise, the approximate feasible region defined by approximate constraints is apt to include some of the infeasible region defined by actual constraints. This can cause the approximate optimum to converge into the infeasible region. In the proposed method, the approximate optimization is performed with the approximate constraints shifted by their deviations, which are calculated using a diagonal quadratic response surface method. This can prevent the approximate optimum from converging into the infeasible region. To fit the objective and constraints into diagonal quadratic models, we select the center and 4 additional points along each axis of design variables as experimental points. The deviation of each function is calculated using the differences between the real and approximate function values at the experimental points. A sequential approximate optimization technique based on the trust region algorithm is adopted to manage approximate models. The proposed approach is validated by solving some design problems. The results of the problems show the effectiveness of the proposed method.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.245-259
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• 2007

This paper studies some properties of the value functions and gives some sufficient and necessary conditions about the presented global error and local error. And it leads to one kind of relationship between iterative points and optimal solution or K-T point.

• Asian Journal for Public Opinion Research
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• v.12 no.2
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• pp.102-121
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• 2024

Trust is essential for tax compliance. Various tax management issues might diminish taxpayer trust. As a result, as a measure of transparency in the services of the Indonesia's Directorate General of Taxes (DGT), a method for filing various taxpayer complaints is necessary. Whistleblowing is a service given by the DGT that accepts taxpayer issues and complaints. It may be accessed on the DGT's official website. This strategy was intended to increase compliance by instilling trust among taxpayers. This study aims to show how whistleblowing affects tax compliance by utilizing trust as a mediating variable. The study relied on 400 questionnaires issued directly to East Java I DGT Region taxpayers. SEM-PLS with the Smart-PLS tool was utilized for data analysis. According to the study's findings, whistleblowing positively impacts tax compliance, and trust partially mediates the effect of whistleblowing on tax compliance. The outcomes of this study provide empirical proof for the Slippery Slope Framework's contention that building trust is an essential technique for increasing taxpayer compliance.

• Proceedings of the Korean Information Science Society Conference
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• 2004.10b
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• pp.697-699
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• 2004

Stochastic Neighbor Embedding(SNE) is a probabilistic method of mapping high-dimensional data space into a low-dimensional representation with preserving neighbor identities. Even though SNE shows several useful properties, the gradient-based naive SNE algorithm has a critical limitation that it is very slow to converge. To overcome this limitation, faster optimization methods should be considered by using trust region method we call this method fast TR SNE. Moreover, this paper presents a couple of useful optimization methods(i.e. conjugate gradient method and Newton's method) to embody fast SNE algorithm. We compared above three methods and conclude that TR-SNE is the best algorithm among them considering speed and stability. Finally, we show several visualizing experiments of TR-SNE to confirm its stability by experiments.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.573-585
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• 2011

SQP method is one of the most important methods for solving nonlinear programming. But it may fail if the quadratic subproblem is inconsistent. In this paper, we propose a modified nonmonotone filter trust region method in which the QP subproblem is consistent. By means of nonmonotone filter, this method has no demand on the penalty parameter which is difficult to obtain. Moreover, the restoration phase is not needed any more. Under reasonable conditions, we obtain the global convergence of the algorithm. Some numerical results are presented.

• Industrial Engineering and Management Systems
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• v.9 no.1
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• pp.10-19
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• 2010

This paper presents an extended computing procedure for the global optimization of the triple response system (TRS) where the response functions are nonconvex (nonconcave) quadratics and the input factors satisfy a radial region of interest. The TRS arising from response surface modeling can be approximated using a nonlinear mathematical program involving one primary (objective) function and two secondary (constraints) functions. An optimization algorithm named triple response surface algorithm (TRSALG) is proposed to determine the global optimum for the nondegenerate TRS. In TRSALG, the Lagrange multipliers of target (secondary) functions are computed by using the Hooke-Jeeves search method, and the Lagrange multiplier of the radial constraint is located by using the trust region (TR) method at the same time. To ensure global optimality that can be attained by TRSALG, included is the means for detecting the degenerate case. In the field of numerical optimization, as the family of TR approach always exhibits excellent mathematical properties during optimization steps, thus the proposed algorithm can guarantee the global optimal solution where the optimality conditions are satisfied for the nondegenerate TRS. The computing procedure is illustrated in terms of examples found in the quality literature where the comparison results with a gradient-based method are used to calibrate TRSALG.

• The Journal of Korea Robotics Society
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• v.5 no.2
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• pp.85-92
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• 2010

In this paper, we propose a digital image stabilization technique using edge detection and Lucas-Kanade optical flow in order to minimize the motion of the shaken image. The accuracy of motion estimation based on block matching technique depends on the size of search window, which results in long calculation time. Therefore it is not applicable to real-time system. In addition, since the size of vector depends on that of block, it is difficult to estimate the motion which is bigger than the block size. The proposed method extracts the trust region using edge detection, to estimate the motion of some critical points in trust region based on Lucas-Kanade optical flow algorithm. The experimental results show that the proposed method stabilizes the shaking of motion image effectively in real time.