• Korean Management Science Review
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• v.21 no.1
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• pp.77-86
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• 2004

In this paper, we present a methodology for solving the multicommodity network flow problems using interior point methods. In our method, the minimum cost network flow problem extracted from the given multicommodity network flow problem is solved by primal-dual barrier method in which normal equations are solved partially using preconditioned conjugate gradient method. Based on the solution of the minimum cost network flow problem, a warm-start point is obtained from which Castro's specialized interior point method for multicommodity network flow problem starts. In the computational experiments, the effectiveness of our methodology is shown.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.13 no.3
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• pp.171-177
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• 2013

This paper presents a fuzzy set method to enforce complementarity constraints (CCs) in a nonlinear interior point method (NIPM)-based optimization. NIPM is a Newton-type approach to nonlinear programming problems, but it adopts log-barrier functions to deal with the obstacle of managing inequality constraints. The fuzzy-enforcement method has been implemented for CCs, which can be incorporated in optimization problems for real-world applications. In this paper, numerical simulations that apply this method to power system optimal power flow problems are included.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.13 no.1
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• pp.41-53
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• 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 Korean Operations and Management Science Society Conference
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• 1996.10a
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• pp.289-292
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• 1996

In Cholesky factorization of the interior point method, dense columns of A matrix make dense Cholesky factor L regardless of sparsity of A matrix. We introduce a method to transform a primal problem to a dual problem in order to preserve the sparsity.

• Journal of the military operations research society of Korea
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• v.24 no.1
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• pp.146-156
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• 1998

Cholesky factorization is known to be inefficient to problems with dense column and network problems in interior point methods. We use the conjugate gradient method and preconditioners to improve the convergence rate of the conjugate gradient method. Several preconditioners were applied to LPABO 5.1 and the results were compared with those of CPLEX 3.0. The conjugate gradient method shows to be more efficient than Cholesky factorization to problems with dense columns and network problems. The incomplete Cholesky factorization preconditioner shows to be the most efficient among the preconditioners.

• Proceedings of the KIEE Conference
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• 2005.11b
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• pp.156-158
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• 2005

This paper presents an Optimal Power Flow (OPF) algorithm using Interior Point Method (IPM) to swiftly and precisely perform the five minute dispatch. This newly suggested methodology is based on Affine Sealing Interior Point Method (AS IPM), which is favorable for large-scale problems involving many constraints. It is also eligible for OPF problems in order to improve the calculation speed and the preciseness of its resultant solutions. Big-M Method is also used to improve the solution stability. Finally, this paper provides a relevant case study to confirm the efficiency of the proposed methodology.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1996.04a
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• pp.24-29
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• 1996

If the LP problem doesn't have the optimal soultion uniquely, the solution fo the primal-dual barrier method converges to the interior point of the optimal face. Therefore, when the optimal vertex solution or the optimal basis is required, we have to perform the additional procedure to recover the optimal basis from the final solution of the interior point method. In this paper the exisiting methods for recovering the optimal basis or identifying the optimal solutions are analyzed and the new methods are suggested. This paper treats the two optimal basis recovery methods. One uses the purification scheme and the simplex method, the other uses the optimal face solutions. In the method using the purification procedure and the simplex method, the basic feasible solution is obtained from the given interior solution and then simplex method is performed for recovering the optimal basis. In the method using the optimal face solutions, the optimal basis in the primal-dual barrier method is constructed by intergrating the optimal solution identification technique and the optimal basis extracting method from the primal-optimal soltion and the dual-optimal solution.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.9 no.3
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• pp.238-243
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• 2009

This paper present same thodology for the classification of power system voltage stability, the trajectory of which to instability is monotonic, using an interior point method based support vector machine(IPMSVM). The SVM based voltage stability classifier canp rovide real-time stability identification only using the local measurement data, without the topological information conventionally used.

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

• Proceedings of the KIEE Conference
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• 2005.07a
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• pp.858-860
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• 2005

This paper presents an Optimal Power Flow (OPF) algorithm using Interior Point Method (IPM) to swiftly and precisely perform the five minute dispatch. This newly suggested methodology is based on Affine Scailing Interior Point Method (AS IPM), which is favorable for large-scale problems involving many constraints. It is also eligible for OPF problems in order to improve the calculation speed and the preciseness of its resultant solutions. Lastly, this paper provides a relevant case study to confirm the efficiency of the proposed methodology.