• 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

• Journal of the Korean Mathematical Society
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• v.48 no.1
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• pp.13-21
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• 2011

In this paper, a pair of Wolfe type nondifferentiable sec-ond order symmetric minimax mixed integer dual problems is formu-lated. Symmetric and self-duality theorems are established under $\eta_1$-bonvexity/$\eta_2$-boncavity assumptions. Several known results are obtained as special cases. Examples of such primal and dual problems are also given.

• Journal of the military operations research society of Korea
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• v.25 no.2
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• pp.97-105
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• 1999

When infeasible interior-point methods are applied to large-scale linear programming problems, they become unstable and cannot solve the problems if convergence rates of primal feasibility, dual feasibility and duality gap are not well-balanced. We can balance convergence rates of primal feasibility, dual feasibility and duality gap by introducing control parameters. As a result, the stability and the efficiency of infeasible interior-point methods can be improved.

• East Asian mathematical journal
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• v.27 no.5
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• pp.539-543
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• 2011

In this paper, we consider an optimization problem which consists a nonconvex quadratic objective function and two nonconvex quadratic constraint functions. We formulate its dual problem with semidefinite constraints, and we establish weak and strong duality theorems which hold between these two problems. And we give an example to illustrate our duality results. It is worth while noticing that our weak and strong duality theorems hold without convexity assumptions.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.6 no.1
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• pp.67-80
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• 2002

We formulate a pair of nondifferentiable symmetric dual variational problems with a square root term. Under invexity assumptions, we establish weak, strong, converse and self duality theorems for our variational problems by using the generalized Schwarz inequality. Also, we give the static case of our nondifferentiable symmetric duality results.

• Proceedings of the Korean Vacuum Society Conference
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• 2011.02a
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• pp.472-472
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• 2011

The capacitive coupled plasma (CCP) has been extensively used in the semiconductor industry because it has not only good uniformity, but also low electron temperature. But CCP source has some problems, such as difficulty in varying the ion bombardment energy separately, low plasma density, and high processing pressure, etc. In this reason, dual frequency CCP has been investigated with a separate substrate biasing to control the plasma parameters and to obtain high etch rate with high etch selectivity. Especially, in this study, we studied on the etching of $SiO_2$ by using the pulse-time modulation in the dual-frequency CCP source composed of 60 MHz/ 2 MHz rf power. By using the combination of high /low rf powers, the differences in the gas dissociation, plasma density, and etch characteristics were investigated. Also, as the size of the semiconductor device is decreased to nano-scale, the etching of contact hole which has nano-scale higher aspect ratio is required. For the nano-scale contact hole etching by using continuous plasma, several etch problems such as bowing, sidewall taper, twist, mask faceting, erosion, distortions etc. occurs. To resolve these problems, etching in low process pressure, more sidewall passivation by using fluorocarbon-based plasma with high carbon ratio, low temperature processing, charge effect breaking, power modulation are needed. Therefore, in this study, to resolve these problems, we used the pulse-time modulated dual-frequency CCP system. Pulse plasma is generated by periodical turning the RF power On and Off state. We measured the etch rate, etch selectivity and etch profile by using a step profilometer and SEM. Also the X-ray photoelectron spectroscopic analysis on the surfaces etched by different duty ratio conditions correlate with the results above.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.14 no.2
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• pp.98-104
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• 2014

Locality-sensitive hashing techniques have been developed to efficiently handle nearest neighbor searches and similar pair identification problems for large volumes of high-dimensional data. This study proposes a locality-sensitive hashing method that can be applied to nearest neighbor search problems for data sets containing both numerical and categorical attributes. The proposed method makes use of dual hashing functions, where one function is dedicated to numerical attributes and the other to categorical attributes. The method consists of creating indexing structures for each of the dual hashing functions, gathering and combining the candidates sets, and thoroughly examining them to determine the nearest ones. The proposed method is examined for a few synthetic data sets, and results show that it improves performance in cases of large amounts of data with both numerical and categorical attributes.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.4
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• pp.723-734
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• 2013

A robust optimization problem, which has a maximum function of continuously differentiable functions as its objective function, continuously differentiable functions as its constraint functions and a geometric constraint, is considered. We prove a necessary optimality theorem and a sufficient optimality theorem for the robust optimization problem. We formulate a Wolfe type dual problem for the robust optimization problem, which has a differentiable Lagrangean function, and establish the weak duality theorem and the strong duality theorem which hold between the robust optimization problem and its Wolfe type dual problem. Moreover, saddle point theorems for the robust optimization problem are given under convexity assumptions.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.22 no.2
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• pp.101-113
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• 2018

The dual singular function method(DSFM) is a numerical algorithm to get optimal solution including corner singularities for Poisson and Helmholtz equations. In this paper, we apply DSFM to solve heat equation which is a time dependent problem. Since the DSFM for heat equation is based on DSFM for Helmholtz equation, it also need to use Sherman-Morrison formula. This formula requires linear solver n + 1 times for elliptic problems on a domain including n reentrant corners. However, the DSFM for heat equation needs to pay only linear solver once per each time iteration to standard numerical method and perform optimal numerical accuracy for corner singularity problems. Because the Sherman-Morrison formula is rather complicated to apply computation, we introduce a simplified formula by reanalyzing the Sherman-Morrison method.

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