• Communications for Statistical Applications and Methods
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• 제19권5호
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• pp.655-662
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• 2012

Classification is an important research field in pattern recognition with high-dimensional predictors. The support vector machine(SVM) is a penalized feature selector and classifier. It is based on the hinge loss function, the non-convex penalty function, and the smoothly clipped absolute deviation(SCAD) suggested by Fan and Li (2001). We developed the algorithm for the multiclass SVM with the SCAD penalty function using the local quadratic approximation. For multiclass problems we compared the performance of the SVM with the $L_1$, $L_2$ penalty functions and the developed method.

• Journal of the Korean Data and Information Science Society
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• 제16권4호
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• pp.1141-1145
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• 2005

In this note, we show that Theorem 2.1[Kybernetika, 28(1992) 45-49], a result of a functional relationship between the membership function of LR fuzzy numbers of T-sum and T-product, remains valid for convex additive generator and concave shape functions L and R with simple proof. We also consider the case for 0-symmetric R fuzzy numbers.

• 대한수학회보
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• 제28권2호
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• pp.163-174
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• 1991

This is a continuation of the author's previous work [17]. In this paper, we consider mainly variational inequalities for single-valued functions. We first obtain a generalization of the variational type inequality of Juberg and Karamardian [10] and apply it to obtain strengthened versions of the Hartman-Stampacchia inequality and the Brouwer fixed point theorem. Next, we obtain fairly general versions of Browder's variational inequality [5] and its subsequent generalizations due to Brezis et al [4], Takahashk [23], Shih and Tan [19], Simons [20], and others. Finally, in this paper, we obtain a variational inequality for non-real locally convex t.v.s. which generalizes a result of Shih and Tan [19].

• Journal of applied mathematics & informatics
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• 제16권1_2호
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• pp.125-142
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• 2004

We analyze the convergence properties of Powell's UOBYQA method. A distinguished feature of the method is its use of two trust region radii. We first study the convergence of the method when the objective function is quadratic. We then prove that it is globally convergent for general objective functions when the second trust region radius p converges to zero. This gives a justification for the use of p as a stopping criterion. Finally, we show that a variant of this method is superlinearly convergent when the objective function is strictly convex at the solution.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제6권2호
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• pp.31-42
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• 2002

Applications of a result by Andrica and Raşa involving twice differentiable mappings for Shannon's and R$\acute{e}$nyi's entropy are given.

• Kyungpook Mathematical Journal
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• 제56권1호
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• pp.161-172
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• 2016

In this paper, we use the Riemann-Liouville fractional integrals to establish several new inequalities for some differantiable mappings that are connected with the celebrated Ostrowski type integral inequality.

• 대한수학회보
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• 제53권2호
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• pp.589-600
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• 2016

In this paper, we propose a new incremental gradient method for solving a regularized minimization problem whose objective is the sum of m smooth functions and a (possibly nonsmooth) convex function. This method uses an adaptive stepsize. Recently proposed incremental gradient methods for a regularized minimization problem need O(mn) storage, where n is the number of variables. This is the drawback of them. But, the proposed new incremental gradient method requires only O(n) storage.

• 대한수학회논문집
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• 제37권3호
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• pp.905-913
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• 2022

We characterize metrizability and submetrizability for point-open, open-point and bi-point-open topologies on C(X, Y), where C(X, Y) denotes the set of all continuous functions from space X to Y ; X is a completely regular space and Y is a locally convex space.

• 호남수학학술지
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• 제43권4호
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• pp.587-596
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• 2021

In this article, using the concept proposed reciently by the author, of a Generalized k-Proportional Fractional Integral Operators with General Kernel, new integral inequalities are obtained for convex functions. It is shown that several known results are particular cases of the proposed inequalities and in the end new directions of work are provided.

• Korean Journal of Mathematics
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• 제31권4호
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• pp.433-444
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• 2023

Given a function f analytic in open disk centred at origin of radius unity and satisfying the condition |f(z)/g(z) - 1| < 1 for a analytic function g with certain prescribed conditions in the unit disk, radii constants R are determined for the values of Rzf'(Rz)/f(Rz) to lie inside the domain enclosed by the curve |w² - 1| = 1 (lemniscate of Bernoulli). This, in turn, provides a partial solution to the conjectures and problems for determination of sharp bounds R for such functions f.