• KSII Transactions on Internet and Information Systems (TIIS)
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• 제10권10호
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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.

• 대한수학회논문집
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• 제31권4호
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• pp.879-893
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• 2016

In this paper, we introduce three subgradient extragradient algorithms for solving pseudomonotone equilibrium problems. The paper originates from the subgradient extragradient algorithm for variational inequalities and the extragradient method for pseudomonotone equilibrium problems in which we have to solve two optimization programs onto feasible set. The main idea of the proposed algorithms is that at every iterative step, we have replaced the second optimization program by that one on a specific half-space which can be performed more easily. The weakly and strongly convergent theorems are established under widely used assumptions for bifunctions.

• 한국경영과학회지
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• 제32권3호
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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 Communications and Networks
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• 제15권5호
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• pp.527-537
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• 2013

Improving resource utilization has been a hot issue in heterogeneous wireless networks (HWNs). This paper proposes a radio resource management (RRM) method based on access proportion optimization. By considering two or more wireless networks in overlapping regions, users in these regions must select one of the networks to access when they engage in calls. Hence, the proportion of service arrival rate that accesses each network in the overlapping region can be treated as an optimized factor for the performance analysis of HWNs. Moreover, this study considers user mobility as an important factor that affects the performance of HWNs, and it is reflected by the handoff rate. The objective of this study is to maximize the total throughput of HWNs by choosing the most appropriate factors. The total throughput of HWNs can be derived on the basis of a Markov model, which is determined by the handoff rate analysis and distribution of service arrival rate in each network. The objective problem can actually be expressed as an optimization problem. Considering the convexity of the objective function, the optimization problem can be solved using the subgradient approach. Finally, an RRM optimization scheme for HWNs is proposed. The simulation results show that the proposed scheme can effectively enhance the throughput of HWNs, i.e., improve the radio resource utilization.

• 경영과학
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• 제25권2호
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• pp.25-42
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• 2008

CDMA/TOD with asymmetric capacity allocation between uplink and downlink is a highly attractive solution to support the next generation mobile systems. This is because flexible asymmetric allocation of capacity to uplink and downlink usually improves the utilization of the limited bandwidth. In this paper, we mathematically formulate an optimal timeslot and code allocation problem, which is to maximize the total utility considering the numbers of codes(channels) allocated to each data class and the forced terminations of previously allocated codes. We also suggest a real-time integrated timeslot and code allocation scheme using Lagrangean relaxation and subgradient optimization techniques. Experimental results show that the proposed scheme provides high-quality solutions in a fast time.

• 한국경영과학회지
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• 제16권2호
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• pp.14-35
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• 1991

The purpose of this study is to develop an efficient exact algorithm for the problem of scheduling n in dependent jobs on m unequal parallel processors to minimize makespan. Efficient solutions are already known for the preemptive case. But for the non-preemptive case, this problem belongs to a set of strong NP-complete problems. Hence, it is unlikely that the polynomial time algorithm can be found. This is the reason why most investigations have bben directed toward the fast approximate algorithms and the worst-case analysis of algorithms. Recently, great advances have been made in mathematical theories regarding Lagrangean relaxation and the subgradient optimization procedure which updates the Lagrangean multipliers. By combining and the subgradient optimization procedure which updates the Lagrangean multipliers. By combining these mathematical tools with branch-and-bound procedures, these have been some successes in constructing pseudo-polynomial time algorithms for solving previously unsolved NP-complete problems. This study applied similar methodologies to the unequal parallel processor problem to find the efficient exact algorithm.

• 한국경영과학회지
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• 제16권2호
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• pp.13-35
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• 1991

The purpose of this study is to develop an efficient exact algorithm for the problem of scheduling n in dependent jobs on m unequal parallel processors to minimize makespan. Efficient solutions are already known for the preemptive case. But for the non-preemptive case, this problem belongs to a set of strong NP-complete problems. Hence, it is unlikely that the polynomial time algorithm can be found. This is the reason why most investigations have bben directed toward the fast approximate algorithms and the worst-case analysis of algorithms. Recently, great advances have been made in mathematical theories regarding Lagrangean relaxation and the subgradient optimization procedure which updates the Lagrangean multipliers. By combining and the subgradient optimization procedure which updates the Lagrangean multipliers. By combining these mathematical tools with branch-and-bound procedures, these have been some successes in constructing pseudo-polynomial time algorithms for solving previously unsolved NP-complete problems. This study applied similar methodologies to the unequal parallel processor problem to find the efficient exact algorithm.

• Journal of applied mathematics & informatics
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• 제23권1_2호
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• pp.361-367
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• 2007

In this paper we propose an implementable method for solving a nonsmooth convex optimization problem by combining Moreau-Yosida regularization, bundle and quasi-Newton ideas. The method we propose makes use of approximate subgradients of the objective function, which makes the method easier to implement. We also prove the convergence of the proposed method under some additional assumptions.

• Journal of applied mathematics & informatics
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• 제28권5_6호
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• pp.1239-1248
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• 2010

In this paper, an implementable BFGS bundle algorithm for solving a nonsmooth convex optimization problem is presented. The typical method minimizes an approximate Moreau-Yosida regularization using a BFGS algorithm with inexact function and the approximate gradient values which are generated by a finite inner bundle algorithm. The approximate subgradient of the objective function is used in the algorithm, which can make the algorithm easier to implement. The convergence property of the algorithm is proved under some additional assumptions.

• 대한산업공학회지
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• 제30권2호
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• pp.93-106
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• 2004

This paper studied a maximal covering location problem with cost restrictions, to maximize level of service within predetermined cost. It is assumed that all demand have to be met. If the demand node is located within a given range, then its demand is assumed to be covered, but if it is not, then its demand is assumed to be uncovered. An uncovered demand is received a service but at an unsatisfactory level. The objective function is to maximize the sum of covered demand, Two heuristics based on the Lagrangean relaxation of allocation and decoupling are presented and tested. Upper bounds are found through a subgradient optimization and lower bounds are by a cutting algorithm suggested in this paper. The cutting algorithm enables the Lagrangean relaxation to be proceeded continually by allowing infeasible solution temporarily when the feasible solution is not easy to find through iterations. The performances are evaluated through computational experiments. It is shown that both heuristics are able to find the optimal solution in a relatively short computational time for the most instances, and that decoupling relaxation outperformed allocation relaxation.