• KSII Transactions on Internet and Information Systems (TIIS)
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• v.10 no.10
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• pp.4864-4882
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• 2016

In this work, we consider the optimization problem of minimizing energy consumption for real-time multicast over wireless multi-hop networks. Previously, a distributed primal-dual subgradient algorithm was used for finding a solution to the optimization problem. However, the traditional subgradient algorithms have drawbacks in terms of i) sensitivity to iteration parameters; ii) need for saving previous iteration results for computing the optimization results at the current iteration. To overcome these drawbacks, using a joint network coding and scheduling optimization framework, we propose a novel distributed primal-dual Random Deflected Subgradient (RDS) algorithm for solving the optimization problem. Furthermore, we derive the corresponding recursive formulas for the proposed RDS algorithm, which are useful for practical applications. In comparison with the traditional subgradient algorithms, the illustrated performance results show that the proposed RDS algorithm can achieve an improved optimal solution. Moreover, the proposed algorithm is stable and robust against the choice of parameter values used in the algorithm.

• Journal of the Korean Operations Research and Management Science Society
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• v.32 no.3
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• pp.33-46
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• 2007

This study deals with the adaptive multiuser OFDM (Orthogonal Frequency Division Multiplexing) system which adjusts the resource allocation according to the environmental changes in such as wireless and quality of service required by users. The resource allocation includes subcarrier assignment to users, modulation method and power used for subcarriers. We first develop a general optimization model which maximizes data throughput while satisfying data rates required by users and total power constraints. Based on the property that this problem has the 0 duality gap, we apply the subgradient dual optimization method which obtains the solution of the dual problem by iteration of simple calculations. Extensive experiments with realistic data have shown that the subgradient dual method is applicable to the real world system, and can be used as a dynamic resource allocation mechanism.

• Journal of Electrical Engineering and Technology
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• v.7 no.1
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• pp.17-22
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• 2012

Lagrangian relaxation is the most widely adopted method for solving unit commitment (UC) problems. It consists of two steps: dual optimization and primal feasible solution construction. The dual optimization step is crucial in determining the overall performance of the solution. This paper intends to evaluate two dual optimization methods - one based on subgradient (SG) and the other based on the cutting plane. Large-scale UC problems with hundreds of thousands of variables and constraints have been generated for evaluation purposes. It is found that the evaluated SG method yields very promising results.

• Journal of Communications and Networks
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• v.12 no.3
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• pp.246-252
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• 2010

A binary linear integer program is formulated for the problem of expanding the capacity of a fiber optic network and routing the traffic to deliver new interactive multimedia services. A two-phase Lagrangian dual search procedure and a Lagrangian heuristic are developed. Computational results show superior performance of the two-phase subgradient optimization compared with the conventional one-phase approach.

• Journal of Korean Institute of Industrial Engineers
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• v.29 no.3
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• pp.206-212
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• 2003

In this paper, we propose a mathematical optimization model with a suitable algorithm to determine delivery and backlogging quantities by minimizing the total cost including the penalty costs for delay. The system has fixed transshipment costs and demands are fulfilled by some delivery units that represent the volume of delivery amount to be shipped in a single time period. Since, backlogging is allowed, demands could be delivered later at the expense of some penalty costs. The model provides the optimal decisions on when and how much to he delivered while minimizing the total costs. To solve the problem, we propose an algorithm that uses the Lagrangian dual in conjunction with some primal heuristic techniques that exploit the special structure of the problem. Finally, we present some computational test results along with comments on the further study.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.32 no.10A
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• pp.1023-1033
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• 2007

This study considers a joint congestion control, routing and power control for energy-constrained wireless networks. A mathematical model is introduced which includes maximization of network utility, maximization of network lifetime, and trade-off between network utility and network lifetime. The framework would maximize the overall throughput of the network where the overall throughput depends on the data flow rates which in turn is dependent on the link capacities. The link capacity on the other hand is a function of transmit power levels and link Signal-to-Interference-plus-Noise-Ratio (SINR) which makes the power allocation problem inherently difficult to solve. Using dual decomposition techniques, subgradient method, and logarithmic transformations, a joint algorithm for rate and power allocation problems was formulated. Numerical examples for each optimization problem were also provided.

• Journal of Communications and Networks
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• v.16 no.5
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• pp.568-577
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• 2014

We consider a mobile content delivery network (mCDN) in which special mobile devices designated as caching servers (caching-server device: CSD) can provide mobile stations with popular contents on demand via device-to-device (D2D) communication links. On the assumption that mobile CSD's are randomly distributed by a Poisson point process (PPP), an optimization problem is formulated to determine the probability of storing the individual content in each server in a manner that minimizes the average caching failure rate. Further, we present a low-complexity search algorithm, optimum dual-solution searching algorithm (ODSA), for solving this optimization problem. We demonstrate that the proposed ODSA takes fewer iterations, on the order of O(log N) searches, for caching N contents in the system to find the optimal solution, as compared to the number of iterations in the conventional subgradient method, with an acceptable accuracy in practice. Furthermore, we identify the important characteristics of the optimal caching policies in the mobile environment that would serve as a useful aid in designing the mCDN.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2006.05a
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• pp.1647-1655
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• 2006

본 연구는 무선 및 사용자요구사항 등 환경의 변화에 따라 부반송파(subcarrier) 할당, 변조방식 및 전력량을 조절하는 적응형 다중사용자 OFDM 시스템을 다룬다. 먼저 사용자별 전송요구 비트수 및 전체 사용가능한 전력량에 대한 제약 조건하에서 총 데이터 전송량(Throughput)을 최대화하는 최적화 문제를 모형화한다. 이 문제는 대부분의 기존 연구들을 포함할 수 있을 정도로 포괄적이지만 미분이 불가능한 비선형 최적화 문제이면서도 빠른 계산시간을 요구한다. 본 연구는 쌍대간격(Duality Gap)이 0이라는 제안 문제의 특성을 바탕으로 하여 Subgradient 쌍대최적화(Dual Optimization) 기법을 적용한다. 또한 이러한 접근법은 사용자 또는 무선환경의 변화에 적극적으로 적응하는 무선자원 할당 메커니즘을 제시한다.

• Management Science and Financial Engineering
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• v.17 no.2
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• pp.1-21
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• 2011

This paper considers an integrated inventory-distribution system with a fleet of heterogeneous vehicles employed where a single warehouse distributes a single type of products to many spatially distributed retailers to satisfy their dynamic demands. The problem is to determine order planning at the warehouse, and also vehicle schedules and delivery quantities for the retailers with the objective of minimizing the sum of ordering cost at the warehouse, inventory holding cost at both the warehouse and retailers, and transportation cost. For the problem, we give a Mixed Integer Programming formulation and develop a Lagrangean heuristic procedure for computing lower and upper bounds on the optimal solution value. The Lagrangean dual problem of finding the best Lagrangrean lower bound is solved by subgradient optimization. Computational experiments on randomly generated test problems showed that the suggested algorithm gives relatively good solutions in a reasonable amount of computation time.

• 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.