• Nonlinear Functional Analysis and Applications
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• 제27권2호
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• pp.223-232
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• 2022

The purpose of the paper is to define f-projection operator to develop the f-projection method. The existence of a variational inequality problem is studied using fixed point theorem which establishes the existence of f-projection method. The concept of ρ-projective operator and σ-involutory operator are defined with suitable examples. The relation in between ρ-projective operator and σ-involutory operator are shown. The concept of σ-involutory variational inequality problem is defined and its existence theorem is also established.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제8권1호
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• pp.55-66
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• 2004

First the notion of the A-monotonicity is applied to the approximation - solvability of a class of nonlinear variational inclusion problems, and then the convergence analysis is given based on a projection-like method. Results generalize nonlinear variational inclusions involving H-monotone mappings in the Hilbert space setting.

• 한국해안·해양공학회논문집
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• 제20권6호
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• pp.553-563
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• 2008

만일 임의의 지형을 다수의 계단으로 근사하면 이 지형 위를 지나는 선형 파랑의 변형을 계산하기 위해 변분근사법과 고유함수 전개법을 사용할 수 있다. 본 논문에서는 반사율과 투과율을 계산하기 위해 변분근사식과 연계된 산란체법을 제시하였다. 본 기법은 O'Hare and Davies의 변환행렬 축차법보다 간단하고 직접적인 방법임을 보였다. 또한 수 개의 수치실험을 실시하여 기존 결과와 거의 같은 결과를 얻었다.

• Journal of applied mathematics & informatics
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• 제29권1_2호
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• pp.227-245
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• 2011

In this paper, we introduce a new iterative method for finding a common element of the set of solutions for mixed equilibrium problem, the set of solutions of the variational inequality for a ${\beta}$inverse-strongly monotone mapping and the set of fixed points of a family of finitely nonexpansive mappings in a real Hilbert space by using the viscosity and Ces$\`{a}$ro mean approximation method. We prove that the sequence converges strongly to a common element of the above three sets under some mind conditions. Our results improve and extend the corresponding results of Kumam and Katchang [A viscosity of extragradient approximation method for finding equilibrium problems, variational inequalities and fixed point problems for nonexpansive mapping, Nonlinear Analysis: Hybrid Systems, 3(2009), 475-86], Peng and Yao [Strong convergence theorems of iterative scheme based on the extragradient method for mixed equilibrium problems and fixed point problems, Mathematical and Computer Modelling, 49(2009), 1816-828], Shimizu and Takahashi [Strong convergence to common fixed points of families of nonexpansive mappings, Journal of Mathematical Analysis and Applications, 211(1) (1997), 71-83] and some authors.

• 대한수학회논문집
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• 제25권2호
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• pp.207-214
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• 2010

In this paper, a generalized variational inequality problem is considered. An iterative method is studied for approximating a solution of the generalized variational inequality problem. Strong convergence theorem are established in a real Hilbert space.

• 한국산학기술학회논문지
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• 제9권5호
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• pp.1249-1254
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• 2008

그래프 모델에서 가장 중요한 부분은 관찰 데이터가 주어진 상황에서 은닉 변수와 더불어 파라미터의 사후확률 분포의 계산이다. 이 논문에서는 가우시안 혼합 모델에 대한 변분 베이지안 방법의 구현과 변분 근사화 분포의 분해 유도를 제안한다. 이 방법은 정보 검색이나 데이터 시각화와 같은 데이터 분석 등에 적용이 가능하다.

• 대한기계학회논문집A
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• 제28권9호
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• pp.1255-1261
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• 2004

A variational approximation procedure is introduced to study the contact stresses between a representative asperity and a feature generally happening in superfinishing processes such as FAM. After a description of the model under consideration is presented, a system of governing equation for the model is derived fullowed by the assumptions made in order to make progress in model development. Final computation is made to evaluate contact stresses on an elastic asperity tip in small scale in size and a computer simulation is performed for detailed surface profile variations on a representative feature. Numerical results are presented along with a discussion of the conclusions that can be drawn from this analysis.

• 한국해안·해양공학회논문집
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• 제21권2호
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• pp.91-107
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• 2009

단일 계단지형 위를 지나는 선형 파랑의 변형을 계산하기 위해 변분근사법과 고유함수 전개법을 사용하였다. 이들 수치해를 비교에서 반사율과 투과율 그리고 해면변위는 거의 일치한다. 그러나 계단 경계에서 유속 정합조건이 부여되었음에도 불구하고 계산된 x방향 유속의 수직구조는 차이를 보인다.

• 호남수학학술지
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• 제15권1호
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• pp.105-120
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• 1993

The auxiliary principle technique is used to prove the uniqueness and the existence of solutions for a class of nonlinear variational inequalities and suggest an innovative iterative algorithm for computing the approximate solution of variational inequalities. Error estimates for the finite element approximation of the solution of variational inequalities are derived, which refine the previous known results. An example is given to illustrate the applications of the results obtained. Several special cases are considered and studied.

• ETRI Journal
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• 제33권6호
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• pp.914-923
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• 2011

This paper concerns robust and reliable speaker model training for text-independent speaker verification. The baseline speaker modeling approach is the Gaussian mixture model (GMM). In text-independent speaker verification, the amount of speech data may be different for speakers. However, we still wish the modeling approach to perform equally well for all speakers. Besides, the modeling technique must be least vulnerable against unseen data. A traditional approach for GMM training is expectation maximization (EM) method, which is known for its overfitting problem and its weakness in handling insufficient training data. To tackle these problems, variational approximation is proposed. Variational approaches are known to be robust against overtraining and data insufficiency. We evaluated the proposed approach on two different databases, namely KING and TFarsdat. The experiments show that the proposed approach improves the performance on TFarsdat and KING databases by 0.56% and 4.81%, respectively. Also, the experiments show that the variationally optimized GMM is more robust against noise and the verification error rate in noisy environments for TFarsdat dataset decreases by 1.52%.