• Earthquakes and Structures
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• v.7 no.1
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• pp.1-15
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• 2014

In this paper we consider three different cases and we apply Variational Approach (VA) to solve the non-natural vibrations and oscillations. The method variational approach does not demand small perturbation and with only one iteration can lead to high accurate solution of the problem. Some patterns are presented for these three different cease to show the accuracy and effectiveness of the method. The results are compared with numerical solution using Runge-kutta's algorithm and another approximate method using energy balance method. It has been established that the variational approach can be an effective mathematical tool for solving conservative nonlinear dynamical equations.

• Communications for Statistical Applications and Methods
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• v.29 no.1
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• pp.27-40
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• 2022

In this paper, the focus on the removal noise in the binary image based on the variational Bayesian method with the Ising model. The observation and the latent variable are the degraded image and the original image, respectively. The posterior distribution is built using the Markov random field and the Ising model. Estimating the posterior distribution is the same as reconstructing a degraded image. MCMC and variational Bayesian inference are two methods for estimating the posterior distribution. However, for the sake of computing efficiency, we adapt the variational technique. When the image is restored, the iterative method is used to solve the recursive problem. Since there are three model parameters in this paper, restoration is implemented using the VECM algorithm to find appropriate parameters in the current state. Finally, the restoration results are shown which have maximum peak signal-to-noise ratio (PSNR) and evidence lower bound (ELBO).

• Communications of the Korean Mathematical Society
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• v.35 no.2
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• pp.517-532
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• 2020

In this paper, we consider a class of nonlocal problems with indefinite weights in Orlicz-Sobolev space. Under some suitable conditions on the nonlinearities, we establish some existence results using variational techniques and Ekeland's variational principle.

• Journal of the Korean Operations Research and Management Science Society
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• v.20 no.2
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• pp.125-137
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• 1995

This paper provides a locally convergent algorithm and a globally convergent algorithm for a variational inequality problem over convex polyhedral. The algorithm are based on the B (ouligand)-differentiability of the solution of a nonsmooth equation derived from the variational in-equality problem. Convergences of the algorithms are achieved by the results of Pang[3].

• Bulletin of the Korean Mathematical Society
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• v.59 no.4
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• pp.1019-1044
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• 2022

In this paper, we propose new algorithms for solving equilibrium and multivalued variational inequality problems in a real Hilbert space. The first algorithm for equilibrium problems uses only one approximate projection at each iteration to generate an iteration sequence converging strongly to a solution of the problem underlining the bifunction is pseudomonotone. On the basis of the proposed algorithm for the equilibrium problems, we introduce a new algorithm for solving multivalued variational inequality problems. Some fundamental experiments are given to illustrate our algorithms as well as to compare them with other algorithms.

• Bulletin of the Korean Mathematical Society
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• v.60 no.6
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• pp.1697-1704
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• 2023

We study a multidimensional nonlinear variational sine-Gordon equation, which can be used to describe long waves on a dipole chain in the continuum limit. By using the method of characteristics, we show that a solution of a nonlinear variational sine-Gordon equation with certain initial data in a multidimensional space has a singularity in finite time.

• Bulletin of the Korean Mathematical Society
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• v.52 no.4
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• pp.1149-1167
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• 2015

We get a theorem which shows the existence of at least four $2{\pi}$-periodic weak solutions for the bifurcation problem of the Hamiltonian system with the superquadratic nonlinearity. We obtain this result by using the variational method, the critical point theory induced from the limit relative category theory.

• Journal of applied mathematics & informatics
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• v.4 no.2
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• pp.433-446
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• 1997

In this paper we study an existence and the approxi-mation of the solution of the solution of the elliptic variational inequality from an abstract axiomatic point of view. We discuss convergence results and give an error estimate for the difference of the two solutions in an appropriate norm Also we present some computational results by using fixed point method.

• Communications of the Korean Mathematical Society
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• v.22 no.2
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• pp.247-258
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• 2007

In this paper a new class of system of generalized nonlinear variational inequalities involving strongly monotone, relaxed co coercive and relaxed generalized monotone mappings in Hilbert spaces is introduced and studied. Based on the projection method, an equivalence between the system of generalized nonlinear variational inequalities and the fixed point problem is established, which is used to suggest some new iterative algorithms for computing approximate solutions of the system of generalized nonlinear variational inequalities. A few sufficient conditions which ensure the existence and uniqueness of solution of the system of generalized nonlinear variational inequalities are given, and the convergence analysis of iterative sequences generated by the algorithms are also discussed.

• Journal of Korea Multimedia Society
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• v.22 no.11
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• pp.1251-1258
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• 2019

Intelligent tutoring system enables users to effectively learn by utilizing various artificial intelligence techniques. For instance, it can recommend a proper curriculum or learning method to individual users based on their learning history. To do this effectively, user's characteristics need to be analyzed and classified based on various aspects such as interest, learning ability, and personality. Even though data labeled by the characteristics are required for more accurate classification, it is not easy to acquire enough amount of labeled data due to the labeling cost. On the other hand, unlabeled data should not need labeling process to make a large number of unlabeled data be collected and utilized. In this paper, we propose a semi-supervised learning method based on feedback variational auto-encoder(FVAE), which uses both labeled data and unlabeled data. FVAE is a variation of variational auto-encoder(VAE), where a multi-layer perceptron is added for giving feedback. Using unlabeled data, we train FVAE and fetch the encoder of FVAE. And then, we extract features from labeled data by using the encoder and train classifiers with the extracted features. In the experiments, we proved that FVAE-based semi-supervised learning was superior to VAE-based method in terms with accuracy and F1 score.