• Journal of the Korean Operations Research and Management Science Society
• /
• v.11 no.2
• /
• pp.37-50
• /
• 1986

In combining dispersed optimization models, either primal or dual(or both) decomposition method widely used as an organizing device. Interpreting the methods economically, the concepts of price and resource-directive coordination are generally well accepted. Most of deomposition/ integration methods utilize either primal information of dual information, not both, from subsystems, while some authors have developed mixed decomposition approaches employing two master problems dealing primal and dual proposals separately. In this paper a hybrid decomposition method is introduced, where one hybrid master problem utilizes the underlying relationships between primal and dual information from each subsystem. The suggested method is well justified with respect to the flexibility in information flow pattern choice (some prices and other quantities) and to the compatibility of subdivision's optimum to the systemwide optimum, that is often lacking in conventional decomposition methods such as Dantzig-Wolfe's. A numerical example is also presented to illustrate the suggested approach.

• Journal of the Korean Operations Research and Management Science Society
• /
• v.9 no.2
• /
• pp.3-8
• /
• 1984

This paper considers the intermediate warehouse location problem in a two stage distribution system where commodities are delivered from the given set of capacitated factories to customers via uncapacitated intermediate warehouses. In order to determine the subset of warehouses to open which minimizes the total distribution costs including the fixed costs associated with opening warehouses, the cross decomposition method for mixed integer programming recently developed by T.J. Van Roy is used. The cross decomposition unifies Benders decomposition and Lagrangean relaxation into a single framework that involves successive solutions to a primal subproblem and a dual subproblem. In our problem model, primal subproblem turns out to be a transshipment problem and dual subproblem turns out to be an intermediate warehouse location problem with uncapacitated factories.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.13 no.1
• /
• pp.41-53
• /
• 2009

A primal-dual interior point method(IPM) not only is the most efficient method for a computational point of view but also has polynomial complexity. Most of polynomialtime interior point methods(IPMs) are based on the logarithmic barrier functions. Peng et al.([14, 15]) and Roos et al.([3]-[9]) proposed new variants of IPMs based on kernel functions which are called self-regular and eligible functions, respectively. In this paper we define a new kernel function and propose a new IPM based on this kernel function which has $O(n^{\frac{2}{3}}log\frac{n}{\epsilon})$ and $O(\sqrt{n}log\frac{n}{\epsilon})$ iteration bounds for large-update and small-update methods, respectively.

• Proceedings of the KIEE Conference
• /
• 2002.07a
• /
• pp.366-368
• /
• 2002

This paper presents a technique that can obtain an optimal solution for the Security-Constrained Economic Dispatch (SCED) problems using the Interior Point Method (IPM) while taking into account of the power flow constraints. The SCED equations are formulated by using only the real power flow equations from the optimal power flow. Then an algorithm is presented that can linearize the SCED equations based on the relationships among generation real power outputs, loads, and transmission losses to obtain the optimal solutions by applying the linear programming (LP) technique. Finally, the application of the Primal Interior Point Method (PIPM) for solving the optimization problem based on the proposed linearized objective function is presented. The results are compared with the Simplex Method and the Promising results ard obtained.

• Journal of the Korean Operations Research and Management Science Society
• /
• v.17 no.1
• /
• pp.3-16
• /
• 1992

We present a modified Tank and Hopfield's neural network model for solving Linear Programming problems. We have found the fact that the Tank and Hopfield's neural circuit for solving Linear Programming problems has some difficulties in guaranteeing convergence, and obtaining both the primal and dual optimum solutions from the output of the circuit. We have identified the exact conditions in which the circuit stops at an interior point of the feasible region, and therefore fails to converge. Also, proper scaling of the problem parameters is required, in order to obtain a feasible solution from the circuit. Even after one was successful in getting a primal optimum solution, the output of the circuit must be processed further to obtain a dual optimum solution. The modified model being proposed in the paper is designed to overcome such difficulties. We describe the modified model and summarize our computational experiment.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.39A no.10
• /
• pp.622-624
• /
• 2014

In this letter, the joint mode selection and resource allocation method is proposed for D2D communication underlaying OFDMA based cellular networks. In the proposed scheme, D2D mode possible region is determined which satisfies QoS. Then we solve the optimization problem utilizing primal-dual algorithm. The proposed scheme shows better performance than conventional schemes.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.4 no.2
• /
• pp.59-66
• /
• 2000

We consider a multiobjective fractional variational programming problem (P) involving vector valued functions. By using the concept of proper efficiency, a relationship between the primal problem and parametric multiobjective variational problem is indicated.

• The Journal of Information Technology
• /
• v.3 no.2
• /
• pp.73-85
• /
• 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 Korean Institute of Industrial Engineers
• /
• v.29 no.3
• /
• pp.206-212
• /
• 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
• /
• v.35 no.5
• /
• pp.569-587
• /
• 2019

In this paper, we consider a split least-squares characteristic mixed element method for Sobolev equations with a convection term. First, to manipulate both convection term and time derivative term efficiently, we apply a characteristic mixed element method to get the system of equations in the primal unknown and the flux unknown and then get a least-squares minimization problem and a least-squares characteristic mixed element scheme. Finally, we obtain a split least-squares characteristic mixed element scheme for the given problem whose system is uncoupled in the unknowns. We prove the optimal order in $L^2$ and $H^1$ normed spaces for the primal unknown and the suboptimal order in $L^2$ normed space for the flux unknown.