• 한국멀티미디어학회논문지
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• 제24권1호
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• pp.13-20
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• 2021

A Wasserstein GAN(WGAN), optimum in terms of minimizing Wasserstein distance, still suffers from inconsistent convergence or unexpected output due to inherent learning instability. It is widely known some kinds of restriction on the discriminative function should be considered to solve such problems, which implies the importance of Lipschitz continuity. Unfortunately, there are few known methods to satisfactorily maintain the Lipschitz continuity of the discriminative function. In this paper we propose techniques to stably maintain the Lipschitz continuity of the discriminative function by adding effective regularization terms to the objective function, which limit the magnitude of the gradient vectors of the discriminator to one or less. Extensive experiments are conducted to evaluate the performance of the proposed techniques, which shows the single-sided penalty improves convergence compared with the gradient penalty at the early learning process, while the proposed additional penalty increases inception scores by 0.18 after 100,000 number of learning.

• 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.

• 대한수학회보
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• 제58권3호
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• pp.745-765
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• 2021

Let Ω be a proper open subset of ℝⁿ and p(·) : Ω → (0, ∞) be a variable exponent function satisfying the globally log-Hölder continuous condition. In this article, the author introduces the "geometrical" variable Hardy spaces H^p(·)_r (Ω) and H^p(·)_z (Ω) on Ω, and then obtains the grand maximal function characterizations of H^p(·)_r (Ω) and H^p(·)_z (Ω) when Ω is a strongly Lipschitz domain of ℝⁿ. Moreover, the author further introduces the "geometrical" variable local Hardy spaces h^p(·)_r (Ω), and then establishes the atomic characterization of h^p(·)_r (Ω) when Ω is a bounded Lipschitz domain of ℝⁿ.

• 충청수학회지
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• 제12권1호
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• pp.119-124
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• 1999

In this paper, T.Kawata's result[2] is generalized, by means of Hausdorff-Young inequality and Beurling's norm.

• Journal of applied mathematics & informatics
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• 제28권1_2호
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• pp.431-438
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• 2010

In this paper, using nonsmooth analysis, we established equivalence results between a locally Lipschitz vector optimization problem and its associated approximated problem under the proper efficiency.

• Korean Journal of Mathematics
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• 제24권3호
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• pp.335-344
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• 2016

In this paper, we obtain quantitative estimates for generalized double Baskakov operators. We calculate global results for these operators using Lipschitz-type spaces and estimate the error using modulus of continuity.

• Journal of the Korean Statistical Society
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• 제27권4호
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• pp.485-494
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• 1998

In the white noise model we construct an adaptive estimate for f(0) for a decreasing function f. We also show that the maximum mean square error of this estimate attains the same rate as the minimax risk simultaneously over a range of Lipschitz classes of order less than or equal to one.

• East Asian mathematical journal
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• 제31권3호
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• pp.301-310
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• 2015

In this paper, we establish a strong convergence for the Noor iterative scheme associated with Lipschitz strongly pseudocontractive mappings in real Banach spaces. It's proof-method is very simple by comparing with the previous proofs known.

• 충청수학회지
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• 제5권1호
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• pp.103-110
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• 1992

In this paper, T. Kawata's result[2] is generalized, by means of Beurling's norm, in the case of periodic stochastic processes of the second order which belong to Lipschitz class.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제13권3호
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• pp.207-215
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• 2006

Using more precise majorizing sequences than before [6], [10], [11], [14] we provide a finer semilocal convergence analysis for a certain class of Euler-Halley type methods for approximating a solution of an equation in a Banach space setting.