• Nonlinear Functional Analysis and Applications
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• v.26 no.4
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• pp.839-853
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• 2021

Let 𝕽ⁿ be an Euclidean space and g : 𝕽ⁿ → 𝕽ⁿ be a monotone and continuous mapping. Suppose the convex constrained nonlinear monotone equation problem x ∈ 𝕮 s.t g(x) = 0 has a solution. In this paper, we construct an inertial-type algorithm based on the three-term derivative-free projection method (TTMDY) for convex constrained monotone nonlinear equations. Under some standard assumptions, we establish its global convergence to a solution of the convex constrained nonlinear monotone equation. Furthermore, the proposed algorithm converges much faster than the existing non-inertial algorithm (TTMDY) for convex constrained monotone equations.

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.1553-1556
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• 1997

In the paper, we porpose a new mehtod of extending PLS(Partial Least Squares) regressiion method to nonlinear framework and apply it to the estimation of product compositions in high-purity distillation column. There have veen similar efforets to overcome drawbacks of PLS by using nonlinear-mapping ability of meural networks, however, they failed to show great improvement over PLS since they focused only in capturing nonlinear functional relationship between input data, not on nonlinear correlation inthe data set. By incorporating the structure of Robust Auto Associative Networks(RAAN) into that of previous nonlinear PLS, we can handle nonlinear correlation as well as nonlinear functional relationship. The application result shows that the proposed method performs better than previous ones even for nonlinearities caused by changing operating conditions, limited observations, and existence of meas-unrement noises.

• Structural Monitoring and Maintenance
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• v.5 no.2
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• pp.261-272
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• 2018

The commonly used TMD design method in the project assumes the TMD has pure linearity. However, in real engineering TMD will exhibit nonlinear behaviors. Without considering the nonlinearity of TMD, the control effect of the TMD that is designed by the linear design method, may be worse and even enlarge the structural response. In this paper, based on the previous study results of nonlinear TMD, the improved design method for engineering application is proposed. The linear design method and the improved design method are compared. Taking the best parameter obtained by the improved design method is less than or equal to 90% of that obtained by the original design method as the dividing line. The critical nonlinear coefficient, reaching which value the improved design method needs to be used, is given. Finally, numerical simulations on two engineering examples are conducted to proof the results.

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1533-1539
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• 2011

In this paper, a class of nonlinear bilevel programs, i.e. the lower level problem is linear programs, is considered. Aiming at this special structure, we append the duality gap of the lower level problem to the upper level objective with a penalty and obtain a penalized problem. Using the penalty method, we give an existence theorem of solution and propose an algorithm. Then, a numerical example is given to illustrate the algorithm.

• Communications of the Korean Mathematical Society
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• v.11 no.4
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• pp.1147-1157
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• 1996

Nonlinear ill-posed problems arise in many application including parameter estimation and inverse scattering. We introduce a least squares regularization method to solve nonlinear ill-posed problems with constraints robustly and efficiently. The regularization method uses Trust-Region approach to handle the constraints on variables. The Generalized Cross Validation is used to choose the regularization parameter in computational tests. Numerical results are given to exhibit faster convergence of the method over other methods.

• 제어로봇시스템학회:학술대회논문집
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• 1991.10a
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• pp.185-190
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• 1991

In this paper, we present a method of analising a system with nonlinear parameter by pole sensitivity defined by the rate of pole movement with respect of non-linear parameter variation. Pole sensitivity give us not only the rate of pole movement but also the directional information. We present a method of design of a state feedback for a system with nonlinear system parameter by considering the pole sensitivity and show that the suggested method guarantee the stability robustness for a system with nonlinear parameter, parameter perturbation and urimodelled dynamics.

• Journal of applied mathematics & informatics
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• v.8 no.3
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• pp.683-691
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• 2001

A linearized finite-difference scheme is used to transform the initial/boundary-value problem associated with the nonlinear Schrodinger equation into a linear algebraic system. This method is developed by replacing the time and the nonlinear term by an appropriate parametric linearized scheme based on Taylor’s expansion. The resulting finite-difference method is analysed for stability and convergence. The results of a number of numerical experiments for the single-soliton wave are given.

• Proceedings of the IEEK Conference
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• 2002.06c
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• pp.33-36
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• 2002

In this paper, we propose a control method of an unknown nonlinear system using a dynamical neural network. The method proposed in this paper performs for a nonlinear system with unknown system, identification with using the dynamical neural network, and then a nonlinear adaptive controller is designed with these identified informations. In order to verify the effectiveness of the proposed algorithm, we simulated one-link manipulator. The simulation result showed the effectiveness of using the dynamical neural network in the adaptive control of one-link manipulator.

• Structural Engineering and Mechanics
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• v.65 no.4
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• pp.409-413
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• 2018

In this paper, He's Variational Approach (VA) is used to solve high nonlinear vibration equations. The proposed approach leads us to high accurate solution compared with other numerical methods. It has been established that this method works very well for whole range of initial amplitudes. The method is sufficient for both linear and nonlinear engineering problems. The accuracy of this method is shown graphically and the results tabulated and results compared with numerical solutions.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.773-781
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• 2010

Recently, Yun [8] proposed a new three-step iterative method with the fourth-order convergence for solving nonlinear equations. By using his ideas, we develop a general form of multi-step iterative methods with higher order convergence for solving nonlinear equations, and then we study convergence analysis of the multi-step iterative methods. Lastly, some numerical experiments are given to illustrate the performance of the multi-step iterative methods.