• 대한수학회보
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• 제54권4호
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• pp.1347-1359
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• 2017

The purpose of this paper is to give some new iterative methods for finding a common zero of a finite family of monotone operators in Hilbert spaces. We also give the applications of the obtained result for the convex feasibility problem and constrained convex optimization problem in Hilbert spaces.

• 대한수학회논문집
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• 제32권2호
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• pp.447-456
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• 2017

The purpose of this paper is to introduce some strong convergence theorems for the problem of finding a common zero of a finite family of monotone operators and the problem of finding a common fixed point of a finite family of nonexpansive in Hilbert spaces by hybrid projection method.

• Nonlinear Functional Analysis and Applications
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• 제27권4호
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• pp.895-902
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• 2022

The aim of this paper is to construct a new method for finding the zeros of the sum of two maximally monotone mappings in Hilbert spaces. We will define a simple function such that its set of zeros coincide with that of the sum of two maximal monotone operators. Moreover, we will use the Newton-Raphson algorithm to get an approximate zero. In addition, some illustrative examples are given at the end of this paper.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 1996년도 봄 학술발표회 논문집
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• pp.182-189
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• 1996

The focus of this study is on the problem of the design of structure of undetermined topology. This problem has been regarded as being the most challenging of structural optimization problems, because of the difficulty of allowing topology to change. Conventional approaches break down when element sizes approach to zero, due to stiffness matrix singularity. In this study, a novel nonlinear Programming formulation of the topology Problem is developed and examined. Its main feature is the ability to account for topology variation through zero element sizes. Stiffness matrix singularity is avoided by embedding the equilibrium equations as equality constraints in the optimization problem. Although the formulation is general, two dimensional plane elasticity examples are presented. The design problem is to find minimum weight of a plane structure of fixed geometry but variable topology, subject to constraints on stress and displacement. Variables are thicknesses of finite elements, and are permitted to assume zero sizes. The examples demonstrate that the formulation is effective for finding at least a locally minimal weight.

• Korean Journal of Mathematics
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• 제27권3호
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• pp.563-580
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• 2019

In this paper, we study the strong metric dimension of zero-divisor graph ${\Gamma}(R)$ associated to a ring R. This is done by transforming the problem into a more well-known problem of finding the vertex cover number ${\alpha}(G)$ of a strong resolving graph $G_{sr}$. We find the strong metric dimension of zero-divisor graphs of the ring ${\mathbb{Z}}_n$ of integers modulo n and the ring of Gaussian integers ${\mathbb{Z}}_n$[i] modulo n. We obtain the bounds for strong metric dimension of zero-divisor graphs and we also discuss the strong metric dimension of the Cartesian product of graphs.

• 대한수학회지
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• 제55권4호
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• pp.849-875
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• 2018

The purpose of this paper is to present an operator method of regularization for the problem of finding a solution of a system of nonlinear ill-posed equations with a monotone hemicontinuous mapping and N inverse-strongly monotone mappings in Banach spaces. A regularization parameter choice is given and convergence rate of the regularized solutions is estimated. We also give the convergence and convergence rate for regularized solutions in connection with the finite-dimensional approximation. An iterative regularization method of zero order in a real Hilbert space and two examples of numerical expressions are also given to illustrate the effectiveness of the proposed methods.

• 전산구조공학
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• 제9권3호
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• pp.169-177
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• 1996

구조물에 있어서 위상학적 최적화 문제는 최적화를 구하는 과정에서 구조체가 변화함으로 인한 어려움 때문에 최적화 분야에서 가장 어려운 문제로 간주되어 왔다. 종래의 방법으로는 일반적으로 구조요소 사이즈가 영으로 접근할 때 강성 매트릭스의 singularity를 발생시킴으로써 최적의 해를 얻지 못하고 도중에 계산이 종료되어 버린다. 본 연구에 있어서는 이러한 문제점들을 해결하기 위한 비선형 프로그래밍 formulation을 제안하는 것을 목적으로 한다. 이 formulation의 주된 특성은 요소 사이즈가 영이 되는 것을 허용한다. 평형방정식을 등제약조건으로 간주함으로써 강성 매트릭스의 singularity를 피할 수 있다. 이 formulation을 하중을 받는 구조물에 있어서 응력과 변위의 제약조건하에서 중량을 최소화할때의 유한요소의 두께를 구하는 디자인 문제에 적용하여, 이 formulation이 위상학적 최적화에 있어서의 효과를 입증하였다.

• 한국공간구조학회논문집
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• 제3권2호
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• pp.101-107
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• 2003

There exists a structural problem for link structures in the unstable state. The primary characteristics of this problem are in the existence of rigid body displacements without strain, and in the possibility of the introduction of prestressing to change an unstable state into a stable state. When we make local linearized incremental equations in order to obtain knowledge about these unstable structures, the determinant of the coefficient matrices is zero, so that we face a numerically unstable situation. This is similar to the situation in the stability problem. To avoid such a difficult situation, in this paper a simple and straightforward method was presented by means of the generalized inverse for the numerical analysis of stability problem.

• ETRI Journal
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• 제21권4호
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• pp.9-22
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• 1999

This paper considers a problem of configuring both physical backbone and logical virtual path (VP) networks in a reconfigurable asynchronous transfer mode (ATM) network where links are subject to failures. The objective is to determine jointly the VP assignment, the capacity assignment of physical links and the bandwidth allocation of VPs, and the routing assignment of traffic demand at least cost. The network cost includes backbone link capacity expansion cost and penalty cost for not satisfying the maximum throughput of the traffic due to link failures or insufficient link capacities. The problem is formulated as a zero-one non-linear mixed integer programming problem, for which an effective solution procedure is developed by using a Lagrangean relaxation technique for finding a lower bound and a heuristic method exploited for improving the upper bound of any intermediate solution. The solution procedure is tested for its effectiveness with various numerical examples.

• 한국정보과학회논문지:시스템및이론
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• 제31권7호
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• pp.397-401
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• 2004

각 에지에 무게(양수, 음수, 0 가능)가 주어진 트리에서, 경로의 에지들의 무게의 합이 비음수이면서 길이가 가장 긴 경로를 구하는 문제를 해결하고자 한다. 차수가 3인 트리에서 가장 긴 비음수 경로를 찾는 Ο(n log n) 시간 알고리즘을 제시한다. n은 트리가 가지는 노드의 수이다.