• The Transactions of the Korean Institute of Electrical Engineers A
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• v.54 no.9
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• pp.457-460
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• 2005

This paper proposes a new Interior Point Method algorithm to improve the computation speed and solution stability, which have been challenging problems for employing the nonlinear Optimal Power Flow. The proposed algorithm is different from the tradition Interior Point Methods in that it adopts the Predictor-Corrector Method. It also accommodates the five minute dispatch, which is highly recommenced in modern electricity market. Finally, the efficiency and applicability of the proposed algorithm is demonstrated with a case study.

• Journal of Korean Institute of Industrial Engineers
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• v.19 no.4
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• pp.3-11
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• 1993

We propose a new dual simplex method using a primal interior point. The dropping variable is chosen by utilizing the primal feasible interior point. For a given dual feasible basis, its corresponding primal infeasible basic vector and the interior point are used for obtaining a decreasing primal feasible point The computation time of moving on interior point in our method takes much less than that od Karmarker-type interior methods. Since any polynomial time interior methods can be applied to our method we conjectured that a slight modification of our method can give a polynomial time complexity.

• Journal of Korean Institute of Industrial Engineers
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• v.21 no.3
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• pp.429-439
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• 1995

The Interior point method in linear programming is classified into two categories the affine-scaling method and the logarithmic barrier method. In this paper, we integrate those methods and implement them in one shared module. First, we analyze the procedures of two interior point methods and then find a unified formula in finding directions to improve the current solution and conditions to terminate the procedure. Second, we build the shared modules which can be used in each interior point method. Then these modules are experimented in NETLIB problems.

• Proceedings of the KIEE Conference
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• 2005.07a
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• pp.852-854
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• 2005

This paper proposes a new Interior Point Method algorithm to improve the computation speed and solution stability, which have been challenging problems for employing the nonlinear Optimal Power Flow. The proposed algorithm is different from the traditional Interior Point Methods in that it adopts the Predictor-Corrector Method. It also accommodates the five minute dispatch, which is highly recommended in modern electricity market. Finally, the efficiency and applicability of the proposed algorithm is demonstrated with a case study.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.119-133
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• 2011

This paper proposes an infeasible interior-point algorithm with full-Newton step for linear programming. We introduce a special self-regular proximity to induce the feasibility step and also to measure proximity to the central path. The result of polynomial complexity coincides with the best-known iteration bound for infeasible interior-point methods, namely, O(n log n/${\varepsilon}$).

• Journal of Advanced Marine Engineering and Technology
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• v.28 no.5
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• pp.801-810
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• 2004

The Primal-Dual Interior-Point (PDIP) method is currently one of the fastest emerging topics in optimization. This method has become an effective solution algorithm for large scale nonlinear optimization problems. such as the electric Optimal Power Flow (OPF) and natural gas and electricity OPF. This study describes major theoretical developments of the PDIP method as well as practical issues related to implementation of the method. A simple quadratic problem with linear equality and inequality constraints

• East Asian mathematical journal
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• v.25 no.2
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• pp.147-151
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• 2009

We use an improved Newton-Kantorovich theorem introduced in [2] to analyze interior point methods. Our approach requires less number of steps than before [5] to achieve a certain error tolerance for both Newton's and Modified Newton's methods.

• Korean Management Science Review
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• v.11 no.3
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• pp.1-11
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• 1994

Recent advances in linear programming solution methodology have focused on interior point methods. This powerful new class of methods achieves significant reductions in computer time for large linear programs and solves problems significantly larger than previously possible. These methods can be examined from points of Fiacco and McCormick's barrier method, Lagrangian duality, Newton's method, and others. This study presents a primal-dual log barrier algorithm of interior point methods for linear programming. The primal-dual log barrier method is currently the most efficient and successful variant of interior point methods. This paper also addresses a Cholesky factorization method of symmetric positive definite matrices arising in interior point methods. A special structure of the matrices, called supernode, is exploited to use computational techniques such as direct addressing and loop-unrolling. Two dense matrix handling techniques are also presented to handle dense columns of the original matrix A. The two techniques may minimize storage requirement for factor matrix L and a smaller number of arithmetic operations in the matrix L computation.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.567-579
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• 2009

Recently, Peng et al. proposed a primal-dual interior-point method with new search direction and self-regular proximity for LP. This new large-update method has the currently best theoretical performance with polynomial complexity of O($n^{\frac{q+1}{2q}}\;{\log}\;{\frac{n}{\varepsilon}}$). In this paper we use this search direction to propose a primal-dual interior-point method for convex quadratic programming (QP). We overcome the difficulty in analyzing the complexity of the primal-dual interior-point methods for convex quadratic programming, and obtain the same polynomial complexity of O($n^{\frac{q+1}{2q}}\;{\log}\;{\frac{n}{\varepsilon}}$) for convex quadratic programming.

• Korean Management Science Review
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• v.21 no.2
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• pp.43-60
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• 2004

Every iteration of interior-point methods of large scale optimization requires computing at least one orthogonal projection. In the practice, symmetric variants of the Gaussian elimination such as Cholesky factorization are accepted as the most efficient and sufficiently stable method. In this paper several specific implementation issues of the symmetric factorization that can be applied for solving such equations are discussed. The code called McSML being the result of this work is shown to produce comparably sparse factors as another implementations in the $MATLAB^{***}$ environment. It has been used for computing projections in an efficient implementation of self-regular based interior-point methods, McIPM. Although primary aim of developing McSML was to embed it into an interior-point methods optimizer, the code may equally well be used to solve general large sparse systems arising in different applications.