• Nonlinear Functional Analysis and Applications
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• 제27권2호
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• pp.223-232
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• 2022

The purpose of the paper is to define f-projection operator to develop the f-projection method. The existence of a variational inequality problem is studied using fixed point theorem which establishes the existence of f-projection method. The concept of ρ-projective operator and σ-involutory operator are defined with suitable examples. The relation in between ρ-projective operator and σ-involutory operator are shown. The concept of σ-involutory variational inequality problem is defined and its existence theorem is also established.

• Journal of applied mathematics & informatics
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• 제4권2호
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• pp.407-418
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• 1997

In this paper we establish the equivalence between the general resolvent equations and variational inequalities. This equiva-lence is used to suggest and analyze a number of iterative algorithms for solving variational inclusions. We also study the convergence criteria of the iterative algorithms. Our results include several pre-viously known results as special cases.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제6권1호
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• pp.67-80
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• 2002

We formulate a pair of nondifferentiable symmetric dual variational problems with a square root term. Under invexity assumptions, we establish weak, strong, converse and self duality theorems for our variational problems by using the generalized Schwarz inequality. Also, we give the static case of our nondifferentiable symmetric duality results.

• Korean Journal of Mathematics
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• 제17권3호
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• pp.331-340
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• 2009

We show the existence of nonconstant periodic solution for the nonlinear Hamiltonian systems with some nonlinearity. We approach the variational method. We use the critical point theory and the variational linking theory for strongly indefinite functional.

• 대한수학회논문집
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• 제25권2호
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• pp.207-214
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• 2010

In this paper, a generalized variational inequality problem is considered. An iterative method is studied for approximating a solution of the generalized variational inequality problem. Strong convergence theorem are established in a real Hilbert space.

• 충청수학회지
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• 제20권3호
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• pp.327-332
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• 2007

A variational inequality defined by the second-order cone is considered, and it is shown that a necessary and sufficient condition for a solution of the variational inequality holds under some regularity condition.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제13권3호
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• pp.197-206
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• 2006

This paper introduces a class of multivalued mixed quasi-variational-like ineqcalities and shows the existence of solutions to the class of quasi-variational-like inequalities in reflexive Banach spaces.

• 인터넷정보학회논문지
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• 제22권2호
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• pp.1-9
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• 2021

전통적으로 대부분의 악성코드는 도메인 전문가에 의해 추출된 특징 정보를 활용하여 분석되었다. 하지만 이러한 특징 기반의 분석방식은 분석가의 역량에 의존적이며 기존의 악성코드를 변형한 변종 악성코드를 탐지하는 데 한계를 가지고 있다. 본 연구에서는 도메인 전문가의 개입 없이도 변종 악성코드의 패밀리를 분류할 수 있는 ResNet-Variational AutoEncder 기반 변종 악성코드 분류 방법을 제안한다. Variational AutoEncoder 네트워크는 입력값으로 제공되는 훈련 데이터의 학습 과정에서 데이터의 특징을 잘 이해하며 정규 분포 내에서 새로운 데이터를 생성하는 특징을 가지고 있다. 본 연구에서는 Variational AutoEncoder의 학습 과정에서 잠재 변수를 추출을 통해 악성코드의 중요 특징을 추출할 수 있었다. 또한 훈련 데이터의 특징을 더욱 잘 학습하고 학습의 효율성을 높이기 위해 전이 학습을 수행했다. ImageNet Dataset으로 사전학습된 ResNet-152 모델의 학습 파라미터를 Encoder Network의 학습 파라미터로 전이했다. 전이학습을 수행한 ResNet-Variational AutoEncoder의 경우 기존 Variational AutoEncoder에 비해 높은 성능을 보였으며 학습의 효율성을 제공하였다. 한편 변종 악성코드 분류를 위한 방법으로는 앙상블 모델인 Stacking Classifier가 사용되었다. ResNet-VAE 모델의 Encoder Network로 추출한 변종 악성코드 특징 데이터를 바탕으로 Stacking Classifier를 학습한 결과 98.66%의 Accuracy와 98.68의 F1-Score를 얻을 수 있었다.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제12권4호
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• pp.239-247
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• 2008

Let $I{\in}C^{1,1}$ be a strongly indefinite functional defined on a Hilbert space H. We investigate the number of the critical points of I when I satisfies two pairs of Torus-Sphere variational linking inequalities and when I satisfies m ($m{\geq}2$) pairs of Torus-Sphere variational linking inequalities. We show that I has at least four critical points when I satisfies two pairs of Torus-Sphere variational linking inequality with $(P.S.)^*_c$ condition. Moreover we show that I has at least 2m critical points when I satisfies m ($m{\geq}2$) pairs of Torus-Sphere variational linking inequalities with $(P.S.)^*_c$ condition. We prove these results by Theorem 2.2 (Theorem 1.1 in [1]) and the critical point theory on the manifold with boundary.

• Journal of applied mathematics & informatics
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• 제28권1_2호
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• pp.465-472
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• 2010

The purpose of this article is to introduce a new generalized class of the Wiener-Hopf equations and a new generalized class of the variational inequalities. Using the projection technique, we show that the generalized Wiener-Hopf equations are equivalent to the generalized variational inequalities. We use this alternative equivalence to suggest and analyze an iterative scheme for finding the solution of the generalized Wiener-Hopf equations and the solution of the generalized variational inequalities. The results presented in this paper may be viewed as significant and improvement of the previously known results. In special, our results improve and extend the resent results of M.A. Noor and Z.Y.Huang[M.A. Noor and Z.Y.Huang, Wiener-Hopf equation technique for variational inequalities and nonexpansive mappings, Appl. Math. Comput.(2007), doi:10.1016/j.amc.2007.02.117].