• Journal of the Korean Mathematical Society
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• v.54 no.2
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• pp.461-477
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• 2017

A dual substructuring method with a penalty term was introduced in the previous works by the authors, which is a variant of the FETI-DP method. The proposed method imposes the continuity not only by using Lagrange multipliers but also by adding a penalty term which consists of a positive penalty parameter ${\eta}$ and a measure of the jump across the interface. Due to the penalty term, the proposed iterative method has a better convergence property than the standard FETI-DP method in the sense that the condition number of the resulting dual problem is bounded by a constant independent of the subdomain size and the mesh size. In this paper, a further study for a dual iterative substructuring method with a penalty term is discussed in terms of its convergence analysis. We provide an improved estimate of the condition number which shows the relationship between the condition number and ${\eta}$ as well as a close spectral connection of the proposed method with the FETI-DP method. As a result, a choice of a moderately small penalty parameter is guaranteed.

• Journal of the Korean Mathematical Society
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• v.57 no.5
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• pp.1267-1286
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• 2020

We pay attention to a coupled problem by a penalty term which is induced from non-overlapping domain decomposition methods based on augmented Lagrangian methodology. The coupled problem is composed by two parts mainly; one is a problem associated with local problems in non-overlapping subdomains and the other is a coupled part over all subdomains due to the penalty term. For the speedup of iterative solvers for the coupled problem, we propose two different types of preconditioners: a block-diagonal preconditioner and an additive Schwarz preconditioner as overlapping domain decomposition methods. We analyze the coupled problem and the preconditioned problems in terms of their condition numbers. Finally we present numerical results which show the performance of the proposed methods.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.21 no.3
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• pp.125-142
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• 2017

In this paper, development of the three-dimensional structural analysis is performed by applying FETI-local method. In the FETI-local method, the penalty term is added as a preconditioner. The OPT-DKT shell element is used in the present structural analysis. Newmark-${\beta}$ method is employed to conduct the dynamic analysis. The three-dimensional FETI-local static structural analysis is conducted. The contour and the displacement of the results are compared following the different number of sub-domains. The computational time and memory usage are compared with respect to the number of CPUs used. The three-dimensional dynamic structural analysis is conducted while applying FETI-local method. The present results show appropriate scalability in terms of the computational time and memory usage. It is expected to improve the computational efficiency by combining the advantages of the original FETI method, i.e., FETI-mixed using the mixed local-global Lagrange multiplier.

• Journal of the Korean Data and Information Science Society
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• v.22 no.1
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• pp.99-105
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• 2011

We propose a semi-supervised learning algorithm based on a form of regularization that incorporates similarity and dissimilarity penalty terms. Our approach uses a graph-based encoding of similarity and dissimilarity. We also present a model-selection method which employs cross-validation techniques to choose hyperparameters which affect the performance of the proposed method. Simulations using two types of dat sets demonstrate that the proposed method is promising.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1221-1234
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• 2009

In this paper, we construct fully discrete discontinuous Galerkin approximations to the solution of linear Sobolev equations. We apply a symmetric interior penalty method which has an interior penalty term to compensate the continuity on the edges of interelements. The optimal convergence of the fully discrete discontinuous Galerkin approximations in ${\ell}^{\infty}(L^2)$ norm is proved.

• Communications for Statistical Applications and Methods
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• v.18 no.3
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• pp.267-275
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• 2011

According to recent studies, Bayesian information criteria(BIC) is proposed to determine the structural dimension of the central subspace through sliced inverse regression(SIR) with high-dimensional predictors. The BIC may be useful in K-means clustering inverse regression(KIR) with high-dimensional predictors. However, the direct application of the BIC to KIR may be problematic, because the slicing scheme in SIR is not the same as that of KIR. In this paper, we present empirical penalty term studies of BIC in KIR to identify the most appropriate one. Numerical studies and real data analysis are presented.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.18 no.4
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• pp.337-350
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• 2014

In this paper, we consider discontinuous Galerkin finite element methods with interior penalty term to approximate the solution of nonlinear parabolic problems with mixed boundary conditions. We construct the finite element spaces of the piecewise polynomials on which we define fully discrete discontinuous Galerkin approximations using the Crank-Nicolson method. To analyze the error estimates, we construct an appropriate projection which allows us to obtain the optimal order of a priori ${\ell}^{\infty}(L^2)$ error estimates of discontinuous Galerkin approximations in both spatial and temporal directions.

• 제어로봇시스템학회:학술대회논문집
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• 1998.10a
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• pp.455-460
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• 1998

We propose robust MILP model for scheduling and design of multiproduct batch processes in this paper. Recent stochastic modeling approaches considering uncertainty have mainly focused on maximization of expected NPV. Robust model concept is applied to generate solution spectrum in which we can select the best solution based on tradeoff between robustness measure and expected NPV. Robustness measure is represented as penalty term in the objective function, which is Upper Partial Mean of NPV. We can quantify solution robustness by this penalty term and maintain model as MILP form to be computationally efficient. An example illustrates the effectiveness of the proposed model. In many cases sufficient robustness can be guaranteed through a little reduction of expected NPV.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.48 no.9
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• pp.1088-1095
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• 1999

This paper presents short-term hydro scheduling method for hydrothermal coordination by genetic algorithms. Hydro scheduling problem has many constraints with fixed final reservoir volume. In this paper, the difficult water balance constraints caused by hydraulic coupling satisfied throughout dynamic decoding method. Adaptive penalizing method was also proposed to handle the infeasible solutions that violate various constraints. In this paper, we proposed GA to solve hydrothermal scheduling with appropriate decoding method and dynamic penalty method. The effectiveness of the proposed method is demonstrated in the case study.

• The Journal of the Acoustical Society of Korea
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• v.43 no.3
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• pp.314-323
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• 2024

Recently, a score-penalty method has been used for the acoustic passive tracking of marine mammals. The interesting aspect of this technique lies in the loss function, which has a penalty term representing the mismatch between the measured signal and the modeled signal, while the traditional time-domain matched-field processing is positively considering the match between them. In this study, we apply the score-penalty method into the depth estimation of a passive target with a known source waveform. Assuming deep ocean environments with uncertainties in the sound speed profile, we evaluate the score-penalty method, comparing it with the time-domain matched field processing method. We shows that the score-penalty method is more accurate than the time-domain matched field processing method in the ocean environment with weak mismatch of sound speed profile, and has better efficiency. However, in the ocean enviroment with strong mismatch of the sound speed profile, the score-penalty method also fails in the depth estimation of a target, similar to the time-domain matched-field processing method.