• 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 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.

• Bulletin of the Korean Mathematical Society
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• v.50 no.5
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• pp.1737-1751
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• 2013

An efficient and stable point collocation scheme based on a meshfree method is studied for the stationary incompressible Navier-Stokes equations. We describe the diffuse derivatives associated with the moving least square method. Using these diffuse derivatives, we propose a point collocation method to fit in solving the Navier-Stokes equations which improves the stability of the direct point collocation scheme. The convergence of the numerical solution is investigated from numerical examples. The driven cavity ow and the backward facing step ow are implemented for the reliability of the scheme. Also, the viscous ow on complicated geometry is successfully calculated such as the ow past a circular cylinder in duct.

• 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.

• 한국태양에너지학회:학술대회논문집
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• 2011.04a
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• pp.299-303
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• 2011

This paper proposes a novel sensorless maximum power point tracking (11PPT) algorithm for PV systems. The method is based on dividing the operating time into several intervals in which the PV terminals are short circuited in one interval and the calculated short-current of the PV is obtained and used to determine the optimum operating point where the maximum output power can be obtained. The proposed MPPT algorithm has been introduced into a current-controlled boost converter whose duty ratio is controlled to the maintain MPP condition. The same sequence is then repeated regularly capturing the PV maximum power. The main advantage of this method is eliminating the current sensor. Meanwhile, this MPPT algorithm reduces the power oscillations around the peak power point which occurs with perturbation and observation algorithms. In addition, the total cost will decrease by removing the current sensor from the PV side. Finally, simulation results confirm the accuracy of the proposed method.

• 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 Electrical Engineering and Technology
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• v.12 no.3
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• pp.1203-1210
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• 2017

Switched-inductor (SL) Z-source three-level inverter is a novel high power topology. The SL based impedance network can boost the input dc voltage to a higher value than the single LC impedance network. However, as all the neutral-point-clamped (NPC) inverters, the SL Z-source three-level inverter has to balance the neutral-point (NP) potential too. The principle of the inverter is introduced and then the effects of NP potential unbalance are analyzed. A NP balancing method is proposed. Other than the methods for conventional NPC inverter without Z-source impedance network, the upper and lower shoot-through durations are corrected by the feedforward compensation factors. With the proposed method, the NP potential is balanced and the voltage boosting ability of the Z-source network is not affected obviously. Simulations are conducted to verify the proposed method.

• The Transactions of the Korean Institute of Electrical Engineers P
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• v.59 no.4
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• pp.423-427
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• 2010

Portable sheet resistance-measuring instrument using the dual-configuration Four-Point Probe method is developed for the purpose of precisely measuring the sheet resistance of conducting thin films. While single-configuration Four-Point Probe method has disadvantages of applying sample size, shape and thickness corrections for a probe spacing, the developed instrument has advantages of no such corrections, little edge effects and measuring simply and accurately the sheet resistance between $0.2\Omega/sq$ and $2k\Omega/sq$.

• Bulletin of the Korean Mathematical Society
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• v.56 no.3
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• pp.757-777
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• 2019

In this paper, we study the convergence analysis of the sequences generated by the proximal point method for an infinite family of pseudo-monotone equilibrium problems in Banach spaces. We first prove the weak convergence of the generated sequence to a common solution of the infinite family of equilibrium problems with summable errors. Then, we show the strong convergence of the generated sequence to a common equilibrium point by some various additional assumptions. We also consider two variants for which we establish the strong convergence without any additional assumption. For both of them, each iteration consists of a proximal step followed by a computationally inexpensive step which ensures the strong convergence of the generated sequence. Also, for this two variants we are able to characterize the strong limit of the sequence: for the first variant it is the solution lying closest to an arbitrarily selected point, and for the second one it is the solution of the problem which lies closest to the initial iterate. Finally, we give a concrete example where the main results can be applied.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.9 no.3
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• pp.941-955
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• 2015

In dual-channel networks (DCNs), all frequency hopping (FH) sequences used for data channels are chosen from the original FH sequence used for the control channel by shifting different initial phases. As the number of data channels increases, the hitting frequency point problem becomes considerably serious because DCNs is non-orthogonal synchronization network and FH sequences are non-orthogonal. The increasing severity of the hitting frequency point problem consequently reduces the resource utilization efficiency. To solve this problem, we propose a novel hitting frequency point collision avoidance method, which consists of a sequence-selection strategy called sliding correlation (SC) and a collision avoidance strategy called keeping silent on hitting frequency point (KSHF). SC is used to find the optimal phase-shifted FH sequence with the minimum number of hitting frequency points for a new data channel. The hitting frequency points and their locations in this optimal sequence are also derived for KSHF according to SC strategy. In KSHF, the transceivers transmit or receive symbol information not on the hitting frequency point, but on the next frequency point during the next FH period. Analytical and simulation results demonstrate that unlike the traditional method, the proposed method can effectively reduce the number of hitting frequency points and improve the efficiency of the code resource utilization.