• 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.

• East Asian mathematical journal
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• v.25 no.1
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• pp.55-68
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• 2009

In this paper we propose new large-update primal-dual inte-rior point algorithms for $P_*(\kappa)$ linear complementarity problems(LCPs). New search directions and proximity measures are proposed based on the kernel function$\psi(t)=\frac{t^{p+1}-1}{p+1}+\frac{e^{\frac{1}{t}}-e}{e}$,$p{\in}$[0,1]. We showed that if a strictly feasible starting point is available, then the algorithm has $O((1+2\kappa)(logn)^{2}n^{\frac{1}{p+1}}log\frac{n}{\varepsilon}$ complexity bound.

• Journal of Korean Institute of Industrial Engineers
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• v.10 no.2
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• pp.37-43
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• 1984

For the polymatroidal network, which has set-constraints on arcs, solution procedures to get the weighted maximal flows are investigated. These procedures are composed of the transformation of the polymatroidal network flow problem into a polymatroid intersection problem and a polymatroid intersection algorithm. A greedy polymatroid intersection algorithm is presented, and an example problem is solved. The greedy polymatroid intersection algorithm is a variation of Hassin's. According to these procedures, there is no need to convert the primal problem concerned into dual one. This differs from the procedures of Hassin, in which the dual restricted problem is used.

• 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.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.12 no.1
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• pp.59-70
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• 1992

Quadratic programming problems(QP) have been widely used as a direction-finding subproblem in the engineering and structural design optimization. To develop an efficient solution algorithm for the QP subproblems, theoretical aspects and numerical behavior of mathematical programming methods that can be used as QP solver are studied and compared. For the solution of both primal and dual QP, Simplex, gradient projection(GRP), and augmented Lagrange multiplier algorithms are investigated and coded. From the numerical study, it is found that the primal GRP algorithm with potential constraint strategy and the dual Simplex algorithm are more attractive and effective than the others. They have theoretical robustness as well. Moreover, primal GRP algorithm is preferable in case the number of constraints is larger than the number of design variables. Favorable features of GRP and Simplex algorithm are merged into a combined algorithm, which is useful in the structural design optimization.

• The Journal of Information Technology
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• v.3 no.2
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• pp.73-85
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• 2000

The efficient algorithms are suggested in this study for solving the multicommodity network flow problems applied to Communications Systems. These problems are typical NP-complete optimization problems that require integer solution and in which the computational complexity increases numerically in appropriate with the problem size. Although the suggested algorithms are not absolutely optimal, they are developed for computationally efficient and produce near-optimal and primal integral solutions. We supplement the traditional Lagrangian method with a price-directive decomposition. It proceeded as follows. First, A primal heuristic from which good initial feasible solutions can be obtained is developed. Second, the dual is initialized using marginal values from the primal heuristic. Generally, the Lagrangian optimization is conducted from a naive dual solution which is set as ${\lambda}=0$. The dual optimization converged very slowly because these values have sort of gaps from the optimum. Better dual solutions improve the primal solution, and better primal bounds improve the step size used by the dual optimization. Third, a limitation that the Lagrangian decomposition approach has Is dealt with. Because this method is dual based, the solution need not converge to the optimal solution in the multicommodity network problem. So as to adjust relaxed solution to a feasible one, we made efficient re-allocation heuristic. In addition, the computational performances of various versions of the developed algorithms are compared and evaluated. First, commercial LP software, LINGO 4.0 extended version for LINDO system is utilized for the purpose of implementation that is robust and efficient. Tested problem sets are generated randomly Numerical results on randomly generated examples demonstrate that our algorithm is near-optimal (< 2% from the optimum) and has a quite computational efficiency.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.13 no.3
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• pp.189-202
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• 2009

In this paper we propose new primal-dual interior point algorithms for $P_*(\kappa)$ linear complementarity problems based on a new class of kernel functions which contains the kernel function in [8] as a special case. We show that the iteration bounds are $O((1+2\kappa)n^{\frac{9}{14}}\;log\;\frac{n{\mu}^0}{\epsilon}$) for large-update and $O((1+2\kappa)\sqrt{n}log\frac{n{\mu}^0}{\epsilon}$) for small-update methods, respectively. This iteration complexity for large-update methods improves the iteration complexity with a factor $n^{\frac{5}{14}}$ when compared with the method based on the classical logarithmic kernel function. For small-update, the iteration complexity is the best known bound for such methods.

• Journal of Electrical Engineering and Technology
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• v.6 no.6
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• pp.786-792
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• 2011

The present paper presents an optimal capacitor placement (OCP) algorithm for voltagestability enhancement. The OCP issue is represented using a mixed-integer problem and a highly nonlinear problem. The hybrid particle swarm optimization (HPSO) algorithm is proposed to solve the OCP problem. The HPSO algorithm combines the optimal power flow (OPF) with the primal-dual interior-point method (PDIPM) and ordinary PSO. It takes advantage of the global search ability of PSO and the very fast simulation running time of the OPF algorithm with PDIPM. In addition, OPF gives intelligence to PSO through the information provided by the dual variable of the OPF. Numerical results illustrate that the HPSO algorithm can improve the accuracy and reduce the simulation running time. Test results evaluated with the three-bus, New England 39-bus, and Korea Electric Power Corporation systems show the applicability of the proposed algorithm.

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1285-1293
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• 2011

We establishes the polynomial convergence of a new class of path-following methods for semidefinite linear complementarity problems (SDLCP) whose search directions belong to the class of directions introduced by Monteiro [9]. Namely, we show that the polynomial iteration-complexity bound of the well known algorithms for linear programming, namely the predictor-corrector algorithm of Mizuno and Ye, carry over to the context of SDLCP.

• Journal of Korea Multimedia Society
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• v.9 no.12
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• pp.1636-1648
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• 2006

In this paper, we propose a new optimization approach to the rate control problem in a wired-cum-wireless network. A primal-dual interior-point(PDIP) algorithm is used to find the solution of the rate optimization problem. We show a comparison between the dual-based(DB) algorithm and PDIP algorithm for solving the rate control problem in the wired-cum-wireless network. The PDIP algorithm performs much better than the DB algorithm. The PDIP can be considered as an attractive method to solve the rate control problem in network. We also present a numerical example and simulation to illustrate our conclusions.