• Title/Summary/Keyword: regularized

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CONVERGENCE OF REGULARIZED SEMIGROUPS

  • Lee, Young S.
    • Korean Journal of Mathematics
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    • v.8 no.2
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    • pp.139-146
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    • 2000
  • In this paper, we discuss convergence theorem for contraction C-regularized semigroups. We establish the convergence of the sequence of generators of contraction regularized semigroups in some sense implies the convergence of the sequence of the corresponding contraction regularized semigroups. Under the assumption that R(C) is dense, we show the convergence of generators is implied by the convergence of C-resolvents of generators.

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REGULARIZED EQUILIBRIUM PROBLEMS IN BANACH SPACES

  • Salahuddin, Salahuddin
    • Korean Journal of Mathematics
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    • v.24 no.1
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    • pp.51-63
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    • 2016
  • In this works, we consider a class of regularized equilibrium problems in Banach spaces. By using the auxiliary principle techniques to suggest some iterative schemes for regularized equilibrium problems and proved the convergence of these iterative methods required either pseudoaccretivity or partially relaxed strongly accretivity.

A Mixed Norm Image Restoration Algorithm Using Multi Regularized Parameters (다중 정규화 매개 변수를 이용한 혼합 norm 영상 복원 방식)

  • 김도령;홍민철
    • Proceedings of the IEEK Conference
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    • 2003.11a
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    • pp.489-492
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    • 2003
  • In this paper, we propose an iterative mixed norm image restoration algorithm using multi regularization parameters. A functional which combines the regularized l$_2$ norm functional and the regularized l$_4$ functional is proposed. The smoothness of each functional is determined by the regularization parameters. Also, a regularization parameter is used to determine the relative importance between the regularized l$_2$ functional and the regularized l$_4$ functional. An iterative algorithm is utilized for obtaining a solution and its convergence is analyzed.

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EXPONENTIAL FORMULA FOR C REGULARIZED SEMIGROUPS

  • LEE, YOUNG S.
    • Honam Mathematical Journal
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    • v.26 no.4
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    • pp.401-409
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    • 2004
  • In this paper, we show that C-resolvent of generator can be represented by Laplace transform and establish an exponential formula for C regularized semigroups whose antiderivatives are exponentially bounded.

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REGULARIZED PENALTY METHOD FOR NON-STATIONARY SET VALUED EQUILIBRIUM PROBLEMS IN BANACH SPACES

  • Salahuddin, Salahuddin
    • Korean Journal of Mathematics
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    • v.25 no.2
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    • pp.147-162
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    • 2017
  • In this research works, we consider the general regularized penalty method for non-stationary set valued equilibrium problem in a Banach space. We define weak coercivity conditions and show that the weak and strong convergence problems of the regularized penalty method.

SYSTEM OF GENERALIZED NONLINEAR REGULARIZED NONCONVEX VARIATIONAL INEQUALITIES

  • Salahuddin, Salahuddin
    • Korean Journal of Mathematics
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    • v.24 no.2
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    • pp.181-198
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    • 2016
  • In this work, we suggest a new system of generalized nonlinear regularized nonconvex variational inequalities in a real Hilbert space and establish an equivalence relation between this system and fixed point problems. By using the equivalence relation we suggest a new perturbed projection iterative algorithms with mixed errors for finding a solution set of system of generalized nonlinear regularized nonconvex variational inequalities.

The Doubly Regularized Quantile Regression

  • Choi, Ho-Sik;Kim, Yong-Dai
    • Communications for Statistical Applications and Methods
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    • v.15 no.5
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    • pp.753-764
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    • 2008
  • The $L_1$ regularized estimator in quantile problems conduct parameter estimation and model selection simultaneously and have been shown to enjoy nice performance. However, $L_1$ regularized estimator has a drawback: when there are several highly correlated variables, it tends to pick only a few of them. To make up for it, the proposed method adopts doubly regularized framework with the mixture of $L_1$ and $L_2$ norms. As a result, the proposed method can select significant variables and encourage the highly correlated variables to be selected together. One of the most appealing features of the new algorithm is to construct the entire solution path of doubly regularized quantile estimator. From simulations and real data analysis, we investigate its performance.

A Spatial Regularization of LDA for Face Recognition

  • Park, Lae-Jeong
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.10 no.2
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    • pp.95-100
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    • 2010
  • This paper proposes a new spatial regularization of Fisher linear discriminant analysis (LDA) to reduce the overfitting due to small size sample (SSS) problem in face recognition. Many regularized LDAs have been proposed to alleviate the overfitting by regularizing an estimate of the within-class scatter matrix. Spatial regularization methods have been suggested that make the discriminant vectors spatially smooth, leading to mitigation of the overfitting. As a generalized version of the spatially regularized LDA, the proposed regularized LDA utilizes the non-uniformity of spatial correlation structures in face images in adding a spatial smoothness constraint into an LDA framework. The region-dependent spatial regularization is advantageous for capturing the non-flat spatial correlation structure within face image as well as obtaining a spatially smooth projection of LDA. Experimental results on public face databases such as ORL and CMU PIE show that the proposed regularized LDA performs well especially when the number of training images per individual is quite small, compared with other regularized LDAs.

TWO STEP ALGORITHM FOR SOLVING REGULARIZED GENERALIZED MIXED VARIATIONAL INEQUALITY PROBLEM

  • Kazmi, Kaleem Raza;Khan, Faizan Ahmad;Shahza, Mohammad
    • Bulletin of the Korean Mathematical Society
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    • v.47 no.4
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    • pp.675-685
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    • 2010
  • In this paper, we consider a new class of regularized (nonconvex) generalized mixed variational inequality problems in real Hilbert space. We give the concepts of partially relaxed strongly mixed monotone and partially relaxed strongly $\theta$-pseudomonotone mappings, which are extension of the concepts given by Xia and Ding [19], Noor [13] and Kazmi et al. [9]. Further we use the auxiliary principle technique to suggest a two-step iterative algorithm for solving regularized (nonconvex) generalized mixed variational inequality problem. We prove that the convergence of the iterative algorithm requires only the continuity, partially relaxed strongly mixed monotonicity and partially relaxed strongly $\theta$-pseudomonotonicity. The theorems presented in this paper represent improvement and generalization of the previously known results for solving equilibrium problems and variational inequality problems involving the nonconvex (convex) sets, see for example Noor [13], Pang et al. [14], and Xia and Ding [19].