• Journal of applied mathematics & informatics
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• v.32 no.1_2
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• pp.211-225
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• 2014

A new class of smoothing functions is introduced in this paper, which includes some important smoothing complementarity functions as its special cases. Based on this new smoothing function, we proposed a smoothing Newton method. Our algorithm needs only to solve one linear system of equations. Without requiring the nonemptyness and boundedness of the solution set, the proposed algorithm is proved to be globally convergent. Numerical results indicate that the smoothing Newton method based on the new proposed class of smoothing functions with ${\theta}{\in}(0,1)$ seems to have better numerical performance than those based on some other important smoothing functions, which also demonstrate that our algorithm is promising.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.401-418
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• 2005

In this paper, a dual algorithm, based on a smoothing function of Bertsekas (1982), is established for solving unconstrained minimax problems. It is proven that a sequence of points, generated by solving a sequence of unconstrained minimizers of the smoothing function with changing parameter t, converges with Q-superlinear rate to a Kuhn-Thcker point locally under some mild conditions. The relationship between the condition number of the Hessian matrix of the smoothing function and the parameter is studied, which also validates the convergence theory. Finally the numerical results are reported to show the effectiveness of this algorithm.

• Journal of applied mathematics & informatics
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• v.8 no.3
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• pp.731-742
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• 2001

A Gaussian smoothing algorithm obtained from a cascade of convolutions with a seven-point kernel is described. We prove that the change of local sums after applying our algorithm to sinusoidal signals is reduced to about two thirds of the change by the binomial coefficients. Hence, our seven point kernel is better than the binomial coefficients when trend curves are needed to be generated. We also prove that if our Gaussian convolution is applied to sinusoidal functions, the amplitude of higher frequencies reduces faster than the lower frequencies and hence that it is a low pass filter.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.56.3-56
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• 2001

This study describes the jump error smoothing scheme with fuzzy logic based on the scalar adaptive filter. The scalar adaptive filter is an useful algorithm for smoothing abrupt jump errors. However, the performances of scalar adaptive algorithm depend on the variance of real signal. So to design an effective algorithm, many informations of real and jump signal are required. In this paper, the fuzzy rules are designed by the analysis of scalar adaptive filter, and then the improved and simplified scheme is developed for smoothing the jump error. Simulations to INS/GPS integrated system show that the proposed method is effective.

• Journal of applied mathematics & informatics
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• v.33 no.3_4
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• pp.387-399
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• 2015

In this paper, a new smoothing approximation to the l₁ exact penalty function for constrained optimization problems (COP) is presented. It is shown that an optimal solution to the smoothing penalty optimization problem is an approximate optimal solution to the original optimization problem. Based on the smoothing penalty function, an algorithm is presented to solve COP, with its convergence under some conditions proved. Numerical examples illustrate that this algorithm is efficient in solving COP.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.133-148
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• 2006

This paper proposes a smoothing method for symmetric conic linear programming (SCLP). We first characterize the central path conditions for SCLP problems with the help of Chen-Harker-Kanzow-Smale smoothing function. A smoothing-type algorithm is constructed based on this characterization and the global convergence and locally quadratic convergence for the proposed algorithm are demonstrated.

• International Journal of Aeronautical and Space Sciences
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• v.18 no.1
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• pp.118-128
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• 2017

In this study, we propose a real time inertial navigation system/global positioning system (INS/GPS) integrated smoothing algorithm based on an extended Kalman filter (EKF) and a position damping loop (PDL) for synthetic aperture radar (SAR). Integrated navigation algorithms usually induce discontinuities due to error correction update by the Kalman filter, which are as detrimental to the performance of SAR as the relative position error. The proposed smoothing algorithm suppresses these discontinuities and also reduces the relative position error in real time. An EKF estimates the navigation errors and sensor biases, and all the errors except for the position error are corrected directly and instantly. A PDL activated during SAR operation period imposes damping effects on the position error estimates, where the estimated position error is corrected smoothly and gradually, which contributes to the real time smoothing and small relative position errors. The residual errors are re-estimated by the EKF to maintain the estimation performance and the stability of the overall loop. The performance improvements were confirmed by Monte Carlo simulations. The simulation results showed that the discontinuities were reduced by 99.8% and the relative position error by 48% compared with a conventional EKF without a smoothing loop, thereby satisfying the basic performance requirements for SAR operation. The proposed algorithm may be applicable to low cost SAR systems which use a conventional INS/GPS without changing their hardware configurations.

• Journal of Institute of Control, Robotics and Systems
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• v.7 no.12
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• pp.1015-1023
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• 2001

error behaviour can be considered as a linear combination of low amplitude random noise and abrupt jumps. The reason of jump appearance can be explained by the semi-shading effects(buildings, trees), jamming, high dynamic of vehicle and so on. This study describes the stand-alone GPS error jump smoothing algorithm which is developed based on the scalar adaptive filter. The algorithm consists of the coarse jump smoothing and the fine jump smoothing. On the coarse smoothing step, GPS velocities or position differences are used as the measurement for the scalar adaptive filter. The purpose of adaptive filter is to smooth the jump errors. The coarse positions are detennined by the integration of smoothed velocities. On the fine smoothing step, the differences between GPS positions and the coarse positions are smoothed by another scalar adaptive filter. The reason of fine smoothing is based on the facts that smoothing accuracy depends on the variance ofusefuJ signa\. The coarse smoothing which deal with the difference of positions provides the rough error removing. So the coarse smoothed velocities can have much more low amplitude than the raw ones. The fine smoothing procedure provides high quality of filtering process. Simulation results show the efficiency of proposed scheme.

• Proceedings of the IEEK Conference
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• 2000.09a
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• pp.545-548
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• 2000

Adaptive array systems are hard to remove all the interferences when incident signals are coherent with a desired signal. In this paper, we propose a modified Duvall beamformer, which performs spatial smoothing using spatial interpolation technique to maintain the degree of freedom. The propose algorithm can minimize the loss on the degree of freedom due to spatial smoothing by forming subarrays with interpolated signals. Simulation results show that the proposed algorithm can remove all the interferences while conventional beamformer cannot.

• Proceedings of the Korean Information Science Society Conference
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• 2003.10a
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• pp.64-66
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• 2003

DNA(Deoxyribo Nucleic Acid)컴퓨팅은 생체분자를 계산의 도구로 이용하는 새로운 계산 방법으로 DNA 정보 저장능력과 DNA의 상보적인 관계를 이용하여 연산을 수행하는 방법이다. 최근에는 DNA 분자들이 갖는 강력한 병렬성을 이용하여 NP-Complete 문제에 적용하는 연구가 많이 시도되고 있다. Adleman이 DNA 컴퓨팅을 이용해 해결한 HPP(Hamilton Path Problem)와는 달리 TSP(Traveling Salesman Problem)는 간선에 가중치가 추가되었기 때문에 DNA 염기배열로 표현하기가 어렵고 또한 염기배열의 길이를 줄이기 위해 고정길이 염기배열을 사용할 경우 가중치가 커지면 효율적이지 못하다. 본 논문에서는 스무딩 알고리즘(smoothing algorithm)을 사용하여 간선의 가중치를 일정한 비율로 줄인 다음 유전자 알고리즘을 사용하여 최적의 염기배열을 찾는 방법을 제안하였다.