• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1239-1248
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• 2010

In this paper, an implementable BFGS bundle algorithm for solving a nonsmooth convex optimization problem is presented. The typical method minimizes an approximate Moreau-Yosida regularization using a BFGS algorithm with inexact function and the approximate gradient values which are generated by a finite inner bundle algorithm. The approximate subgradient of the objective function is used in the algorithm, which can make the algorithm easier to implement. The convergence property of the algorithm is proved under some additional assumptions.

• Journal of applied mathematics & informatics
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• v.26 no.3_4
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• pp.493-500
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• 2008

In this paper, we first construct a mathematical model for tagSNP selection based on LD measure $r^2$, then aiming at this kind of model, we develop an efficient algorithm, which is called approximate greedy algorithm. This algorithm is able to make up the disadvantage of the greedy algorithm for tagSNP selection. The key improvement of our approximate algorithm over greedy algorithm lies in that it adds local replacement(or local search) into the greedy search, tagSNP is replaced with the other SNP having greater similarity degree with it, and the local replacement is performed several times for a tagSNP so that it can improve the tagSNP set of the local precinct, thereby improve tagSNP set of whole precinct. The computational results prove that our approximate greedy algorithm can always find more efficient solutions than greedy algorithm, and improve the tagSNP set of whole precinct indeed.

• Speech Sciences
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• v.11 no.2
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• pp.211-216
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• 2004

In this paper, we present a fast encoding algorithm for vector quantization with an approximate Euclidean distance calculation. An approximation is performed by converting floating point to the near integer. An inequality between the approximate Euclidean distance and the nearest distance is developed to avoid unnecessary distance calculations. Since the proposed algorithm rejects those codewords that are impossible to be the nearest codeword, it produces the same output as conventional full search algorithm.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.29 no.1 s.232
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• pp.45-52
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• 2005

A general approximate optimization technique by sequential design domain(SDD) did not save response values for getting an approximate function in each step. It has a disadvantage at aspect of an expense. In this paper, previous response values are recycled for constructing an approximate function. For this reason, approximation function is more accurate. Accordingly, even if we did not determine move limit, a system is converged to the optimal design. Size and shape optimization using approximate optimization technique is carried out with SDD. Algorithm executing Pro/Engineer and ANSYS are automatically adopted in the approximate optimization program by SDD. Convergence criterion is defined such that optimal point must be located within SDD during the three steps. The PLBA(Pshenichny-Lim-Belegundu-Arora) algorithm is used to solve approximate optimization problems. This algorithm uses the second-order information in the direction finding problem and uses the active set strategy.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1131-1141
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• 2010

We develop an algorithm for computing a sparse approximate inverse for a nonsymmetric positive definite matrix based upon the FFAPINV algorithm. The sparse approximate inverse is computed in the factored form and used to work with some Krylov subspace methods. The preconditioner is breakdown free and, when used in conjunction with Krylov-subspace-based iterative solvers such as the GMRES algorithm, results in reliable solvers. Some numerical experiments are given to show the efficiency of the preconditioner.

• Journal of the Korean Society of Safety
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• v.26 no.4
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• pp.80-86
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• 2011

Structural optimization algorithm of steel box girder bridges using improved higher-order approximate reanalysis technique is proposed in this paper. The proposed approximation method is a generalization of the convex approximation method. The order of the approximate reanalysis for each function is analytically adjusted in the optimization process. This self-adjusted capability makes the approximate structural analysis values conservative enough to maintain the optimum design point of the approximate problem. The efficiency of proposed optimazation algorithm, compared with conventional algorithm, is successfully demonstrated in the steel box girder bridges. The efficiency and robustness of proposed algorithm is also demonstrated in practical steel box girder bridges.

• Journal of KIISE:Databases
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• v.27 no.2
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• pp.199-208
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• 2000

The k-nearest neighbor search query based on similarity is very important for content-based multimedia information retrieval(MIR). The conventional exact k-nearest neighbor search algorithm is not efficient for the MIR application because multimedia data should be represented as high dimensional feature vectors. Thus, an approximate k-nearest neighbor search algorithm is required for the MIR applications because the performance increase may outweigh the drawback of receiving approximate results. For this, we propose a new approximate k-nearest neighbor search algorithm for high dimensional data. In addition, the comparison of the conventional algorithm with our approximate k-nearest neighbor search algorithm is performed in terms of retrieval performance. Results show that our algorithm is more efficient than the conventional ones.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.29 no.6 s.237
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• pp.842-851
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• 2005

In this paper, a new method for constrained optimization of noisy functions is proposed. In approximate optimization using response surface methods, if constraints have severe noise, the approximate feasible region defined by approximate constraints is apt to include some of the infeasible region defined by actual constraints. This can cause the approximate optimum to converge into the infeasible region. In the proposed method, the approximate optimization is performed with the approximate constraints shifted by their deviations, which are calculated using a diagonal quadratic response surface method. This can prevent the approximate optimum from converging into the infeasible region. To fit the objective and constraints into diagonal quadratic models, we select the center and 4 additional points along each axis of design variables as experimental points. The deviation of each function is calculated using the differences between the real and approximate function values at the experimental points. A sequential approximate optimization technique based on the trust region algorithm is adopted to manage approximate models. The proposed approach is validated by solving some design problems. The results of the problems show the effectiveness of the proposed method.

• Bulletin of the Korean Mathematical Society
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• v.59 no.4
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• pp.1019-1044
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• 2022

In this paper, we propose new algorithms for solving equilibrium and multivalued variational inequality problems in a real Hilbert space. The first algorithm for equilibrium problems uses only one approximate projection at each iteration to generate an iteration sequence converging strongly to a solution of the problem underlining the bifunction is pseudomonotone. On the basis of the proposed algorithm for the equilibrium problems, we introduce a new algorithm for solving multivalued variational inequality problems. Some fundamental experiments are given to illustrate our algorithms as well as to compare them with other algorithms.

• The Journal of Information Systems
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• v.17 no.3
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• pp.39-58
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• 2008

Mixed Chinese Postman Problem (MCPP) is a practical generalization of the classical Chinese Postman Problem (CPP) and it could be applied in many real world. Although MCPP is useful in terms of reality, MCPP has been proved to be a NP-complete problem. To find optimal solutions efficiently in MCPP, we can reduce searching space to be small effective searching space containing optimal solutions. We propose GENIIS methodology, which is a kind of hybrid algorithm combines the approximate algorithms and genetic algorithm. To get good solutions in the effective searching space, GENIIS uses approximate algorithm and genetic algorithm. This paper validates the usefulness of the proposed approach in a simulation. The results of our paper could be utilized to increase the efficiencies of network and transportation in business.