• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.18 no.1
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• pp.17-26
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• 2014

This paper presents development of an improved domain decomposition method for large scale structural problem that aims to provide high computational efficiency. In the previous researches, we developed the domain decomposition algorithm based on augmented Lagrangian formulation and proved numerical efficiency under both serial and parallel computing environment. In this paper, new computational analysis by the proposed domain decomposition method is performed. For this purpose, reduction in computational time achieved by the proposed algorithm is compared with that obtained by the dual-primal FETI method under serial computing condition. It is found that the proposed methods significantly accelerate the computational speed for a linear structural problem.

• Journal of applied mathematics & informatics
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• v.30 no.5_6
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• pp.759-772
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• 2012

In this paper, semi-infinite constrained programming, a class of constrained nonsmooth optimization problems, are transformed into unconstrained nonsmooth convex programs under the help of exact penalty function. The unconstrained objective function which owns the primal-dual gradient structure has connection with $\mathcal{VU}$-space decomposition. Then a $\mathcal{VU}$-space decomposition method can be applied for solving this unconstrained programs. Finally, the superlinear convergence algorithm is proved under certain assumption.

• Journal of the Korean Operations Research and Management Science Society
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• v.25 no.1
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• pp.27-36
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• 2000

We perform a computational complexity analysis of a heuristic algotithm proposed in the literature for the combinatorial optimization problems extended with a single side-constraint. This algorithm, although such a view was not given in the original work, is a disguised version of an optimal Lagrangian dual solution technique. It also has been observed to be a very efficient heuristic producing near-optimal solutions for the primal problems in some experiments. Especially, the number of iterations grows sublinearly in terms of the network node size so that the heuristic seems to be particularly suitable for the applicatons such as routing with semi-real time requirements. The goal of this paper is to establish a polynomal worst-case complexity of the algorithm. In particular, the obtained complexity bound suports the sublinear growth of the required iterations.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.7 no.2
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• pp.288-307
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• 2013

This paper formulates resource allocation for decode-and-forward (DF) relay assisted multi-cell orthogonal frequency division multiple (OFDM) networks as an optimization problem taking into account of inter-cell interference and users fairness. To maximize the transmit rate of system we propose a joint interference coordination, subcarrier and power allocation algorithm. To reduce the complexity, this semi-distributed algorithm divides the primal optimization into three sub-optimization problems, which transforms the mixed binary nonlinear programming problem (BNLP) into standard convex optimization problems. The first layer optimization problem is used to get the optimal subcarrier distribution index. The second is to solve the problem that how to allocate power optimally in a certain subcarrier distribution order. Based on the concept of equivalent channel gain (ECG) we transform the max-min function into standard closed expression. Subsequently, with the aid of dual decomposition, water-filling theorem and iterative power allocation algorithm the optimal solution of the original problem can be got with acceptable complexity. The third sub-problem considers dynamic co-channel interference caused by adjacent cells and redistributes resources to achieve the goal of maximizing system throughput. Finally, simulation results are provided to corroborate the proposed algorithm.

• Journal of Communications and Networks
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• v.16 no.2
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• pp.121-129
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• 2014

The trend of an increasing demand for a high-quality user experience, coupled with a shortage of radio resources, has necessitated more advanced wireless techniques to cooperatively achieve the required quality-of-experience enhancement. In this study, we investigate the critical problem of rate splitting in heterogeneous cellular networks, where concurrent transmission, for instance, the coordinated multipoint transmission and reception of LTE-A systems, shows promise for improvement of network-wide capacity and the user experience. Unlike most current studies, which only deal with spectral efficiency enhancement, we implement an optimal rate splitting strategy to improve both spectral efficiency and energy efficiency by exploring and exploiting cooperation diversity. First, we introduce the motivation for our proposed algorithm, and then employ the typical cooperative bargaining game to formulate the problem. Next, we derive the best response function by analyzing the dual problem of the defined primal problem. The existence and uniqueness of the proposed cooperative bargaining equilibrium are proved, and more importantly, a distributed algorithm is designed to approach the optimal unique solution under mild conditions. Finally, numerical results show a performance improvement for our proposed distributed cooperative rate splitting algorithm.

• Korean Management Science Review
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• v.11 no.3
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• pp.13-26
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• 1994

In this paper we studied an integration scheme of some simplex algorithms and some efficient techniques to get the stable solution in linear programming code. And we developed a linear programming package (LPAK) by introducing this scheme and techniques. In LPAK three different algorithms were integrated, which were two primal simplex algorithms using Two phase method and big-M method respectively, and the dual simplex algorithm. LPAK introduces several heuristic techniques in each step of simplex method in order to enhance the stability and efficiency. They were new heuristic methods in structuring initial basis, choosing entering variable, choosing dropping variable and performing reinversion. The experimental results on the NETLIB problems showed that LPAK provided the stable solutions.

• Journal of Korean Society for Quality Management
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• v.5 no.1
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• pp.23-29
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• 1977

Geometric programming is very useful for the solution of certain nonlinear programming problems in which the objective function and the constraints are posynomial expressions. By solving the dual program, it can be obtained that the solution of the primal program of Geometric programming. And, more efficient solution is to form an Augmented program possessing degree of difficult zero. A regional water-quality management problem may involve a multistage constrained optimization with many decision variables. In this problem, especially, appling that solution to it is also useful. This paper is described that : 1) the efficient solution of a water-quality management model formed by Geometric programming and 2) the algorithm developed to apply easily a real system by modifing and simplifing the solution.

• Journal of Communications and Networks
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• v.15 no.1
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• pp.102-110
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• 2013

This paper considers a cooperative orthogonal frequency division multiple access (OFDMA)-based cognitive radio network where the primary system leases some of its subchannels to the secondary system for a fraction of time in exchange for the secondary users (SUs) assisting the transmission of primary users (PUs) as relays. Our aim is to determine the cooperation strategies among the primary and secondary systems so as to maximize the sum-rate of SUs while maintaining quality-of-service (QoS) requirements of PUs. We formulate a joint optimization problem of PU transmission mode selection, SU (or relay) selection, subcarrier assignment, power control, and time allocation. By applying dual method, this mixed integer programming problem is decomposed into parallel per-subcarrier subproblems, with each determining the cooperation strategy between one PU and one SU. We show that, on each leased subcarrier, the optimal strategy is to let a SU exclusively act as a relay or transmit for itself. This result is fundamentally different from the conventional spectrum leasing in single-channel systems where a SU must transmit a fraction of time for itself if it helps the PU's transmission. We then propose a subgradient-based algorithm to find the asymptotically optimal solution to the primal problem in polynomial time. Simulation results demonstrate that the proposed algorithm can significantly enhance the network performance.

• International Journal of Aeronautical and Space Sciences
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• v.16 no.2
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• pp.177-189
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• 2015

This paper presents an all-direct domain decomposition approach for large-scale structural analysis. The proposed approach achieves computational robustness and efficiency by enforcing the compatibility of the displacement field across the sub-domain boundaries via local Lagrange multipliers and augmented Lagrangian formulation (ALF). The proposed domain decomposition approach was compared to the existing FETI approach in terms of the computational time and memory usage. The parallel implementation of the proposed algorithm was described in detail. Finally, a preliminary validation was attempted for the proposed approach, and the numerical results of two- and three-dimensional problems were compared to those obtained through a dual-primal FETI approach. The results indicate an improvement in the performance as a result of the implementing the proposed approach.

• Journal of Energy Engineering
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• v.11 no.4
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• pp.291-298
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• 2002

This paper presents a practical methodology that can analysis power flow and marginal factors based on optimal power flow (OPF) of power systems under restructuring environment. First of all, to evaluate useful marginal factors, nonlinear optimization problems of minimum fuel cost and minimum transmission loss are formulated and solved by nonlinear primal-dual interior point method. Here, physical constraints considered in the optimization problems are the limits of bus voltage. line overloading, and real & reactive power generation. Also, an evaluation method of marginal price and marginal transmission loss is presented based on sensitivities calculated by the two OPF problems. Especially, to reflect the cost related to transmission losses in the competitive electricity market, an analysis method of MLF (marginal loss factor) is pro-posed. Numerical results on IEEE RTS 24 show that the proposed algorithm is effective and useful for analysis of power market price.