• 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.

• The Korean Journal of Applied Statistics
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• v.34 no.1
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• pp.9-23
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• 2021

In the following paper we introduce a variational Bayes method that approximates posterior distributions with mean-field method. In particular, we introduce automatic differentiation variation inference (ADVI), which approximates joint posterior distributions using the product of Gaussian distributions after transforming parameters into real coordinate space, and then apply it to pharmacokinetic models that are models for the study of the time course of drug absorption, distribution, metabolism and excretion. We analyze real data sets using ADVI and compare the results with those based on Markov chain Monte Carlo. We implement the algorithms using Stan.

• Journal of applied mathematics & informatics
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• v.7 no.2
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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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• v.29 no.3_4
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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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• v.29 no.2
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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.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.17 no.12
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• pp.2793-2799
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• 2013

This paper proposes an effective feature compensation method to improve speech recognition performance in time-varying background noise condition. The proposed method employs principal component analysis to improve the variational model composition method. The proposed method is employed to generate multiple environmental models for the PCGMM-based feature compensation scheme. Experimental results prove that the proposed scheme is more effective at improving speech recognition accuracy in various SNR conditions of background music, compared to the conventional front-end methods. It shows 12.14% of average relative improvement in WER compared to the previous variational model composition method.

• Journal of Applied and Pure Mathematics
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• v.6 no.3_4
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• pp.177-189
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• 2024

In this paper, we suggest and analyze new higher order classes of iterative methods for solving nonlinear equations by using variational iteration technique. We present several examples to illustrate the efficiency of the proposed methods. Comparison with other similar methods is also given. New methods can be considered as an alternative of the existing methods. This technique can be used to suggest a wide class of new iterative methods for solving nonlinear equations.

• Nonlinear Functional Analysis and Applications
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• v.27 no.1
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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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• v.17 no.1_2_3
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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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• v.27 no.1_2
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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].