• Nonlinear Functional Analysis and Applications
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• 제26권2호
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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.

• 응용통계연구
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• 제34권1호
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• pp.9-23
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• 2021

본 논문에서는 평균장 방법(mean-field methods)을 기반으로 사후 분포(posterior distribution)를 근사하는 방법인 변분 베이즈 방법(variational Bayes methods)에 대해 소개한다. 특히, 모수들을 실수공간으로 변환 후의 결합 사후분포를 가우시안 분포(Gaussian distribution)들의 곱(product)으로 근사하는 방법인 자동 미분 변분 추론(automatic differentiation variational inference)방법에 대해 자세히 소개하고, 환자에게 약물을 투여한 후 시간에 따라 약물의 흐름을 파악하는 연구인 약물동태학 모형(pharmacokinetic models)에 적용한다. 소개된 변분 베이즈 방법을 이용하여 자료분석을 실시하고 마코프 체인 몬테 카를로(Markov chain Monte Carlo)방법을 기초로한 자료분석의 결과와 비교한다. 알고리즘의 구현은 Stan을 이용한다.

• Journal of applied mathematics & informatics
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• 제7권2호
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• pp.483-491
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• 2000

In this paper, we use the auxiliary principle technique to suggest and analyze a class of predictor-corrector methods for solving noncoercive mixed variational inequalities. The convergence of the proposed method requires only the partially relaxed strongly monotonicity. which is even weaker than the co-coercivity. As special cases, we obtain a number of new and known results for classical variational inequalities.

• Journal of applied mathematics & informatics
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• 제29권3_4호
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• pp.603-619
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• 2011

To the best of our knowledge, it would probably be the first time in the literature that we clarify the relationship between Yamada's method and viscosity iteration correctly. We design iterative methods based on the hybrid steepest descent algorithms for solving variational inclusions, equilibrium problems. Our results unify, extend and improve the corresponding results given by many others.

• Nonlinear Functional Analysis and Applications
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• 제29권2호
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• pp.517-526
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• 2024

In this paper, some iterative methods are used to discuss the behavior of general mixed-harmonic variational inequalities. We employ the auxiliary principle technique and g-strongly harmonic monotonicity of the operator to obtain results on the existence of solutions to a generalized class of mixed harmonic variational inequality.

• 한국정보통신학회논문지
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• 제17권12호
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• pp.2793-2799
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• 2013

본 논문에서는 시간에 따라 변하는 잡음 환경에 강인한 음성 인식을 위해 효과적인 특징 보상 기법을 제안한다. 제안하는 기법에서는 기존의 Variational 모델 생성 기법의 모델 정확도를 향상시키고자 PCA를 도입한다. 제안된 기법은 다중 모델을 사용하는 PCGMM 기반의 특징 보상에 적용된다. 실험 결과는 제안한 PCA 기반의 Variational 모델 생성 기법이 배경 음악 환경의 다양한 SNR 조건에서 기존의 전처리 기법에 비하여 음성 인식 성능을 향상 시키는데 우수함을 입증한다. 제안한 모델 생성 기법이 기존의 Variational 모델 생성 방법에 비해 배경 음악 환경에서 평균 12.14%의 상대적 인식 성능 향상률을 나타낸다.

• Nonlinear Functional Analysis and Applications
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• 제27권1호
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• pp.121-140
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• 2022

In this paper, we study the strong convergence of new methods for solving classical variational inequalities problems involving semistrictly quasimonotone and Lipschitz-continuous operators in a real Hilbert space. Three proposed methods are based on Tseng's extragradient method and use a simple self-adaptive step size rule that is independent of the Lipschitz constant. The step size rule is built around two techniques: the monotone and the non-monotone step size rule. We establish strong convergence theorems for the proposed methods that do not require any additional projections or knowledge of an involved operator's Lipschitz constant. Finally, we present some numerical experiments that demonstrate the efficiency and advantages of the proposed methods.

• Journal of applied mathematics & informatics
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• 제17권1_2_3호
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• pp.59-72
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• 2005

The auxiliary principle is used to suggest and analyze some iterative methods for solving solving hemivariational inequalities under mild conditions. The results obtained in this paper can be considered as a novel application of the auxiliary principle technique. Since hemivariational in­equalities include variational inequalities and nonlinear optimization problems as special cases, our results continue to hold for these problems.

• Journal of applied mathematics & informatics
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• 제27권1_2호
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• pp.431-440
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• 2009

In this paper, we introduce and consider a new system of relaxed cocoercive variational inequalities involving three different operators and the concept of projective nonexpansive mapping. Base on the projection technique, we suggest two kinds of new iterative methods for the approximate solvability of this system. The results presented in this paper extend and improve the main results of [S.S. Chang, H.W.J. Lee, C.K. Chan, Generalized system for relaxed co coercive variational inequalities in Hilbert spaces, Appl. Math. Lett. 20 (2007) 329-334] and [Z. Huang, M. Aslam Noor, An explicit projection method for a system of nonlinear variational inequalities with different ($\gamma,r$)-cocoercive mappings, Appl. Math. Comput. (2007), doi:10.1016/j.amc.2007.01.032].

• 응용통계연구
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• 제35권3호
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• pp.445-455
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• 2022

본 논문에서는 고차원 희소 회귀분석을 위한 기존의 베이지안 방법들을 소개하고, 다양한 모의실험 세팅에서 성능을 비교한다. 특히, 확장 가능하고 정확한 베이지안 추론을 가능하게 하는 변분 베이즈 방법(variational Bayes method) (Ray와 Szabó, 2021) 에 중점을 둔다. 시뮬레이션 자료를 기반으로 한 희소 고차원 선형회귀분석을 실시하고 변분 베이즈 방법의 성능을 다른 베이지안 및 빈도론 방법들과 비교한다. 로지스틱 회귀분석에서 변분 베이즈 방법의 실제 성능을 확인하기 위해 백혈병 유전자 발현 자료를 사용하여 실자료 분석을 수행한다.