• Journal of the Korean Society of Manufacturing Process Engineers
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• v.7 no.1
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• pp.38-46
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• 2008

Design technology and speciality production technology to manufacture high quality valve are insufficient in Korea. In order to design the experiments using Taguchi method and Variational Technology Also, from verification of the response model with optimized results was confirmed that usefulness and reliance of application Taguchi method and Variational Technology to structural's optimum design using Taguchi method and Variational Technology.

• East Asian mathematical journal
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• v.27 no.5
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• pp.585-595
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• 2011

In this paper, we introduce and study a new class of strongly nonlinear variational-like inequalities. Under suitable conditions, we prove the existence of solutions for the class of strongly nonlinear variational- like inequalities. By making use of the auxiliary principle technique, we suggest an iterative algorithm for the strongly nonlinear variational-like inequality and give the convergence criteria of the sequences generated by the iterative algorithm.

• East Asian mathematical journal
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• v.26 no.5
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• pp.671-680
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• 2010

A system of nonlinear variational inclusions involving general H-monotone operators in Banach spaces is introduced. Using the resolvent operator technique, we suggest an iterative algorithm for finding approximate solutions to the system of nonlinear variational inclusions, and establish the existence of solutions and convergence of the iterative algorithm for the system of nonlinear variational inclusions.

• Honam Mathematical Journal
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• v.40 no.3
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• pp.509-519
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• 2018

In this paper, we introduce a new class of reciprocal convex set which is called as relative reciprocal convex set. We establish a necessary and sufficient condition for the minimum of the differentiable relative reciprocal convex function. This condition can be viewed as a new class of variational inequality which is called relative reciprocal variational inequality. Using the auxiliary principle technique we discuss the existence criteria for the solution of relative reciprocal variational inequality. Some special cases which are naturally included in our main results are also discussed.

• ETRI Journal
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• v.33 no.6
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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%.

• Bulletin of the Korean Mathematical Society
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• v.42 no.4
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• pp.739-756
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• 2005

The paper presents new collectively fixed point theorems, minimax and quasi-variational inequalities for maps in the S-KKM class.

• Journal of the Korean Mathematical Society
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• v.50 no.4
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• pp.797-811
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• 2013

In this paper, we establish the existence results for second order singular Dirichlet problems via variational methods. Some recent results are extended and improved. Examples are also given to illustrate the new results.

• Nonlinear Functional Analysis and Applications
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• v.28 no.1
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• pp.135-173
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• 2023

The purpose of this paper is to introduce and study a method for solving the split equality of variational inequality and f, g-fixed point problems in reflexive real Banach spaces, where the variational inequality problems are for uniformly continuous pseudomonotone mappings and the fixed point problems are for Bregman relatively f, g-nonexpansive mappings. A strong convergence theorem is proved under some mild conditions. Finally, a numerical example is provided to demonstrate the effectiveness of the algorithm.

• Nonlinear Functional Analysis and Applications
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• v.29 no.2
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• pp.393-418
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• 2024

In this paper, we propose a new inertial subgradient extragradient algorithm with a new linesearch technique that combines the inertial subgradient extragradient algorithm and the KrasnoselskiiMann algorithm. Under some suitable conditions, we prove a weak convergence theorem of the proposed algorithm for finding a common element of the common solution set of a finitely many variational inequality problem and the fixed point set of a nonexpansive mapping in real Hilbert spaces. Moreover, using our main result, we derive some others involving systems of variational inequalities. Finally, we give some numerical examples to support our main result.

• Nonlinear Functional Analysis and Applications
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• v.29 no.2
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• pp.307-332
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• 2024

Two inertial extragradient-type algorithms are introduced for solving convex pseudomonotone variational inequalities with fixed point problems, where the associated mapping for the fixed point is a 𝜌-demicontractive mapping. The algorithm employs variable step sizes that are updated at each iteration, based on certain previous iterates. One notable advantage of these algorithms is their ability to operate without prior knowledge of Lipschitz-type constants and without necessitating any line search procedures. The iterative sequence constructed demonstrates strong convergence to the common solution of the variational inequality and fixed point problem under standard assumptions. In-depth numerical applications are conducted to illustrate theoretical findings and to compare the proposed algorithms with existing approaches.