• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.433-455
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• 2005

Fritz John, and Karush-Kuhn-Tucker type optimality conditions for a constrained variational problem involving higher order derivatives are obtained. As an application of these Karush-Kuhn-Tucker type optimality conditions, Wolfe and Mond-Weir type duals are formulated, and various duality relationships between the primal problem and each of the duals are established under invexity and generalized invexity. It is also shown that our results can be viewed as dynamic generalizations of those of the mathematical programming already reported in the literature.

• Korean Journal of Mathematics
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• v.23 no.3
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• pp.457-478
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• 2015

In this paper we propose an iteration hybrid method for approximating a point in the intersection of the solution-sets of pseudomonotone equilibrium and variational inequality problems and the fixed points of a semigroup-nonexpensive mappings in Hilbert spaces. The method is a combination of projection, extragradient-Armijo algorithms and Manns method. We obtain a strong convergence for the sequences generated by the proposed method.

• Bulletin of the Korean Mathematical Society
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• v.50 no.3
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• pp.777-786
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• 2013

The purpose of this paper is to establish some relationships between proper efficiency of set-valued optimization problems and proper efficiency of vector variational-like inequalities under the assumptions of generalized cone-preinvexity. Our results extend and improve the corresponding results in the literature.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2008.10a
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• pp.263-266
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• 2008

This paper is concerned with the analysis of elasto-plastic stress waves in a mode I semi-infinite cracked solid subjected to Heaviside pulse load. This study adopts a time-discontinuous variational integrator based on Hamiltonian in order to reduce the numerical dispersive and dissipative errors. This also utilizes an integration scheme of the constitutive model with 2nd-order accuracy which is formulated on the strain space for a rate and temperature dependent material model. Finite element analyses of elasto-plastic stress waves are carried out in order to compare the accuracy between a conventional Galerkin method and the time- discontinuous variational integrator.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 2017.06a
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• pp.250-253
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• 2017

본 논문에서는 동시적 위치 추정 및 지도 작성 (simultaneous localization and mapping)에서 루프 폐쇄 검출을 딥러닝 방법의 일종인 variational autoencoder 를 이용하여 수행하는 방법에 대해 살펴본다. Autoencoder 는 비감독 학습 방법의 일종으로 입력 영상이 신경망을 통과하여 얻은 출력 영상과 동일하도록 신경망을 학습시키는 모델이다. 이 때 autoencoder 중간의 병목 지역을 통과함에도 불구하고 입력과 동일한 영상을 계산해야 하는 제약조건이 있기 때문에 이는 차원 축소나 데이터 추상화의 목적으로 많이 사용된다. 여기서 한 단계 더 발전된 variational autoencoder 는 기존의 autoencoder 가 가진 단점인 입력 변수의 분포와 잠재 변수의 분포 사이에 상관관계가 없다는 단점을 해결하기 위해 Kullback-Leibler divergence 를 활용한 손실 함수를 정의하여 사용했다. 실험결과에서는 루프 폐쇄 검출에서 많이 사용되는 City-Centre 와 New College 데이터 집합을 사용하여 평가하였으며 루프 폐쇄 검출의 결과는 정밀도와 재현율을 계산하여 나타냈다.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1343-1359
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• 2009

In this paper, we implement a relatively new analytical technique by combining the traditional variational iteration method and the decomposition method which is called as the variational decomposition method (VDM) for solving the sixth-order boundary value problems. The proposed technique is in fact the modification of variatioanal iteration method by coupling it with the so-called Adomian's polynomials. The analytical results of the equations have been obtained in terms of convergent series with easily computable components. Comparisons are made to verify the reliability and accuracy of the proposed algorithm. Several examples are given to check the efficiency of the proposed algorithm. We have also considered an example where the VDM is not reliable.

• Journal of Information Processing Systems
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• v.15 no.6
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• pp.1296-1305
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• 2019

To solve the problem of poor noise suppression capability and frequent loss of edge contour and detailed information in current fusion methods, an infrared and visible light image fusion method based on variational multiscale decomposition is proposed. Firstly, the fused images are separately processed through variational multiscale decomposition to obtain texture components and structural components. The method of guided filter is used to carry out the fusion of the texture components of the fused image. In the structural component fusion, a method is proposed to measure the fused weights with phase consistency, sharpness, and brightness comprehensive information. Finally, the texture components of the two images are fused. The structure components are added to obtain the final fused image. The experimental results show that the proposed method displays very good noise robustness, and it also helps realize better fusion quality.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2008.05a
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• pp.231-234
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• 2008

This paper is concerned with the analysis of elasto-plastic stress waves by a time discontinuous variational integrator based on Hamiltonian in order to more accurate results in one dimensional dynamic problem. The proposed algorithm adopts both time-discontinuous variational integrator and space-continuous Hamiltonian so as to capture discontinuities of stress waves. This study enables to preserve total mechanical energy such as internal energy, kinetic energy and dissipative energy due to plastic deformation for long integration time. Finite element analysis of elasto-plastic stress waves is carried out in order to demonstrate the accuracy of the proposed algorithm.

• Nonlinear Functional Analysis and Applications
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• v.26 no.2
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• pp.347-371
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• 2021

A plethora of applications from mathematical programmings, such as minimax, mathematical programming, penalization and fixed point problems can be framed as variational inequality problems. Most of the methods that used to solve such problems involve iterative methods, that is why, in this paper, we introduce a new extragradient-like method to solve pseudomonotone variational inequalities in a real Hilbert space. The proposed method has the advantage of a variable step size rule that is updated for each iteration based on previous iterations. The main advantage of this method is that it operates without the previous knowledge of the Lipschitz constants of an operator. A strong convergence theorem for the proposed method is proved by letting the mild conditions on an operator 𝒢. Numerical experiments have been studied in order to validate the numerical performance of the proposed method and to compare it with existing methods.

• Journal of Information Processing Systems
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• v.19 no.3
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• pp.275-288
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• 2023

Many image edge details are easily lost in the image denoising process, and the smooth image regions are prone to produce jagged. In this paper, we propose a wavelet-based image global k- singular value decomposition variational method to remove image noise. A layer of wavelet decomposition is applied to the noisy image first. Then, the image global k-singular value decomposition (IGK-SVD) method is used to remove the random noise of low-frequency components. Furthermore, a constructed variational denoising method (VDM) removes the random noise in the high-frequency component. Finally, the denoised image is obtained by wavelet reconstruction. The experimental results show that the proposed method's peak signal-to-noise ratio (PSNR) value is higher than other methods, and its structural similarity (SSIM) value is closer to one, indicating that the proposed method can effectively suppress image noise while retaining more image edge details. The denoised image has better denoising effects.