• Proceedings of the Korean Society of Computer Information Conference
• /
• 2019.01a
• /
• pp.87-88
• /
• 2019

본 논문에서는 D2D 송수신 단말쌍을 결정하는 방법을 쌍대적 관점에서 살펴보기로 한다. 주어진 D2D 송신단말 그룹과 수신단말 그룹에서 에너지 최적화를 위한 D2D 송수신 단말쌍 할당은 송신단말 그룹이 수신단말 그룹이 되고, 수신단말 그룹이 송신단말 그룹이 되는 환경에서도 동일한 송수신 단말쌍이 할당되는 쌍대적 특성이 있음을 증명하도록 한다.

• The Korean Journal of Applied Statistics
• /
• v.17 no.1
• /
• pp.119-134
• /
• 2004

Generally to estimate the priority vector in AHP, an eigen-vector method or a log-arithmic least square method is applied to pairwise comparison matrix itself. In this paper an estimating method is suggested, which is applied to pairwise comparison matrix adjusted by using the eigen-decomposition of skew-symmetric matrix. We also show theoretical background, meanings, and several advantages of this method by example. This method may be useful in case that pairwise comparison matrix is quite inconsistent.

• Proceedings of the Korean Statistical Society Conference
• /
• 2000.11a
• /
• pp.181-186
• /
• 2000

완전이면교배를 블록화하는 디자인으로 대개 부분적으로 균형된 불완비 블록계획을 사용한다. 이때 블록화하는 디자인으로 삼각형 PBIBD를 사용하기 위해는 대응되는 삼각형 PBIBD를 찾아야 한다. 특정한 모수를 갖는 균형된 불완비 블록계획의 쌍대계획이 삼각형 PBIBD가 되는 성질을 이용하면 삼각형 PBIBD를 새로 찾아야 하는 번거로움 없이 블록 완전이면교배를 설계할 수 있다. 이를 만족하는 블록 완전이면교배를 설계하는 방법과 디자인을 제시하였다.

• Journal of Elementary Mathematics Education in Korea
• /
• v.17 no.2
• /
• pp.351-370
• /
• 2013

The purpose of this study is to analyze the modes of visualization which appears in the process of thinking that mathematically gifted 6th grade students get to understand components of the three-dimensional shapes on the duality of regular polyhedrons, find the duality relation between the relations of such components, and further explore on whether such duality relation comes into existence in other regular polyhedrons. The results identified in this study are as follows: First, as components required for the process of exploring the duality relation of polyhedrons, there exist primary elements such as the number of faces, the number of vertexes, and the number of edges, and secondary elements such as the number of vertexes gathered at the same face and the number of faces gathered at the same vertex. Second, when exploring the duality relation of regular polyhedrons, mathematically gifted students solved the problems by using various modes of spatial visualization. They tried mainly to use visual distinction, dimension conversion, figure-background perception, position perception, ability to create a new thing, pattern transformation, and rearrangement. In this study, by investigating students' reactions which can appear in the process of exploring geometry problems and analyzing such reactions in conjunction with modes of visualization, modes of spatial visualization which are frequently used by a majority of students have been investigated and reactions relating to spatial visualization that a few students creatively used have been examined. Through such various reactions, the students' thinking in exploring three dimensional shapes could be understood.

• Journal of Korean Society of Steel Construction
• /
• v.10 no.4 s.37
• /
• pp.657-666
• /
• 1998

This study presents an effective dual algorithm for the optimal design of steel structures with displacement constraints. The dual method can replace a primary optimization problem with a sequence of approximate explicit subproblems with a simple algebraic structure. Since being convex and separable, each subproblem can be solved efficiently by the dual method. Specifically, this study uses the principle of virtual work to obtain the displacement constraint equations with an explicit form and adds the linear regression equation expressing the relationships between the cross-section properties to the dual algorithm to reduce the number of design variables. Furthermore, this study deals with the discrete optimization problem to select members with the standard steel sections. Through numerical analyses, the proposed method will be compared with the conventional optimality criteria method.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.35 no.3
• /
• pp.259-266
• /
• 2011

We present a new dual sequential approximate optimization (SAO) algorithm called SD-TDQAO (sequential dual two-point diagonal quadratic approximate optimization). This algorithm solves engineering optimization problems with a nonlinear objective and nonlinear inequality constraints. The two-point diagonal quadratic approximation (TDQA) was originally non-convex and inseparable quadratic approximation in the primal design variable space. To use the dual method, SD-TDQAO uses diagonal quadratic explicit separable approximation; this can easily ensure convexity and separability. An important feature is that the second-derivative terms of the quadratic approximation are approximated by TDQA, which uses only information on the function and the derivative values at two consecutive iteration points. The algorithm will be illustrated using mathematical and topological test problems, and its performance will be compared with that of the MMA algorithm.

• Computational Structural Engineering
• /
• v.11 no.4
• /
• pp.229-237
• /
• 1998

본 연구는 횡변위 구속조건을 받는 고층철골구조물의 이산형 최적설계를 위해 효율적인 쌍대알고리즘을 제시하고자 한다. 양함수형태의 횡변위 구속조건을 설정하기 위해 가상일의 원리가 적용되면 고층철골조의 설계변수의 수를 줄여주기 위해 쌍대알고리즘내에 단면특성관계식이 추가된다. 이 알고리즘의 검증을 위하여 횡하중을 받는 네 가지 형태의 고층철골조 예제가 제시되며, 반복과정에서 수렴된 최종물량을 기존의 최적설계방법과 비교해 봄으로써 제시된 알고리즘의 효율성이 검토된다.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.36 no.11A
• /
• pp.878-891
• /
• 2011

We consider the throughput-maximization problem for both the up- and downlink in a wireless network with interference channels. For this purpose, we design an iterative and distributive uplink algorithm based on Lagrangian relaxation. Using the uplink power prices and network duality, we achieve throughput-maximization in the dual downlink that has a symmetric channel and an equal power budget compared to the uplink. The network duality we prove here is a generalized version of previous research [10], [11]. Computational tests show that the performance of the up- and downlink throughput for our algorithms is close to the optimal value for the channel orthogonality factor, ${\theta}{\in}$(0.5, 1]. On the other hand, when the channels are slightly orthogonal (${\theta}{\in}$(0, 0.5]), we observe some throughput degradation in the downlink. We have extended our analysis to the real downlink that has a nonsymmetric channel and an unequal power budget compared to the uplink. It is shown that the modified duality-based approach is thoroughly applied to the real downlink. Considering the complexity of the algorithms in [6] and [18], we conclude that these results are quite encouraging in terms of both performance and practical applicability of the generalized duality theorem.

• Journal of Korean Society of Industrial and Systems Engineering
• /
• v.9 no.13
• /
• pp.45-50
• /
• 1986

본 연구에서 고찰한 surrogate relaxation은 Lagrangian relaxation 방법과는 달리 제약식들을 선형조합으로 묶어 문제를 푼다. 수리계획 분계가 convexity를 만족하지 못하는 경우에는 Lagrangian의 경우와 마찬가지로 surrogate gap이 발생한다. Lagrangian 쌍대이론을 토대로 surrogate optimality condition을 알아보고 수리계획법의 특별 형태인 정수선형계획법에 적용해 보았다. 일반적으로 surrogate gap은 Lagrangian gap 보다 작기 때문에 좀더 근사하게 원 문제의 최적 목적 함수값에 접근할 수 있다. 따라서 branch and bound 알고리즘을 개발할 때 중요한 정보를 제공하는 것이다.

• Communications of the Korean Mathematical Society
• /
• v.15 no.2
• /
• pp.233-255
• /
• 2000

이 논문에서 계치부분군의 일반화와 이들을 이용한 G-열의 도입과정을 다룬다. 계치부분군과 일반화된 계치부분군 그리고 호모토피군의 차이를 설명하여 몇가지 공간의 계치부분군을 계산한다. 그리고 G-열이 완전열이 되기 위한 조건들을 조사하고 이 완전성을 이용하여 계치부분군의 계산과 함수의 단사성과 그 함수의 G-열의 완전성과의 상호 관련성을 보인다. 마지막으로 G-열의 일반화와 쌍대 G-열의 다룬다.