• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.25 no.3
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• pp.107-116
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• 2021

We introduce optimization algorithms using Bregman Divergence for solving non-negative matrix factorization (NMF) problems. Bregman divergence is known a generalization of some divergences such as Frobenius norm and KL divergence and etc. Some algorithms can be applicable to not only NMF with Frobenius norm but also NMF with more general Bregman divergence. Matrix Factorization is a popular non-convex optimization problem, for which alternating minimization schemes are mostly used. We develop the Bregman proximal gradient method applicable for all NMF formulated in any Bregman divergences. In the derivation of NMF algorithm for Bregman divergence, we need to use majorization/minimization(MM) for a proper auxiliary function. We present algorithmic aspects of NMF for Bregman divergence by using MM of auxiliary function.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.7 no.4
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• pp.566-576
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• 1995

A Computational code has been developed in order to design axial fans by the numerical optimization techniques incorporated with flow analysis code solving three-dimensional Navier-Stokes equation. The steepest descent method and the conjugate gradient method are used to look for the search direction in the design space, and the golden section method is used for one-dimensional search. To solve the constrained optimization problem, sequential unconstrained minimization technique, SUMT, is used with imposed quadratic extended interior penalty functions. In the optimization of two-dimensional cascade design, the ratio of drag coefficient to lift coefficient is minimized by the design variables such as maximum thickness, maximum ordinate of camber and chord wise position of maximum ordinate. In the application of this numerical optimization technique to the design of an axial fan, the efficiency is maximized by the design variables related to the sweep angle distributed by quadratic function along the hub to tip of fan.

• Journal of the Korean Institute of Intelligent Systems
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• v.21 no.1
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• pp.12-18
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• 2011

In this paper, we proposed Interval Type-2 polynomial Radial Basis Function Neural Networks. In the receptive filed of hidden layer, Interval Type-2 fuzzy set is used. The characteristic of Interval Type-2 fuzzy set has Footprint Of Uncertainly(FOU), which denotes a certain level of robustness in the presence of un-known information when compared with the type-1 fuzzy set. In order to improve the performance of proposed model, we used the linear polynomial function as connection weight of network. The parameters such as center values of receptive field, constant deviation, and connection weight between hidden layer and output layer are optimized by Conjugate Gradient Method(CGM) and Space Search Evolutionary Algorithm(SSEA). The proposed model is applied to gas furnace dataset and its result are compared with those reported in the previous studies.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.24 no.10
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• pp.1335-1342
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• 2000

Three-dimensional flow analysis and numerical optimization methods are presented for the design of an axial-flow fan. Steady, incompressible, three-dimensional Reynolds-averaged Navier-Stokes equations are used as governing equations, and standard k- ${\varepsilon}$ turbulence model is chosen as a turbulence model. Governing equations are discretized using finite volume method. Steepest descent method, conjugate gradient method and BFGS method are compared to determine the searching directions. Golden section method and quadratic fit-sectioning method are tested for one dimensional search. Objective function is defined as a ratio of generation rate of the turbulent kinetic energy to pressure head. Two variables concerning sweep angle distribution are selected as the design variables. Performance of the final fan designed by the optimization was tested experimentally.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.7 no.9
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• pp.2284-2298
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• 2013

In this paper, a fast and efficient signal reconstruction algorithm for solving the basis pursuit (BP) problem in compressed sensing (CS) is proposed. This fast linearized Bregman method (FLBM), which is inspired by the fast method of Beck et al., is based on the fact that the linearized Bregman method (LBM) is equivalent to a gradient descent method when applied to a certain formulation. The LBM requires $O(1/{\varepsilon})$ iterations to obtain an ${\varepsilon}$-optimal solution while the FLBM reduces this iteration complexity to $O(1/\sqrt{\varepsilon})$ and requiring almost the same computational effort on each iteration. Our experimental results show that the FLBM can be faster than some other existing signal reconstruction methods.

• 유체기계공업학회:학술대회논문집
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• 1999.12a
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• pp.221-226
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• 1999

Three-dimensional flow analysis and numerical optimization methods are presented for the design of an axial-flow fan. Steady, Incompressible, three-dimensional Reynolds-averaged Wavier-Stokes equations are used as governing equations, and standard k-$\epsilon$ turbulence model is chosen as a turbulence model. Governing equations are discretized using finite volume method. Steepest descent method, conjugate gradient method and BFGS method are compared to determine the searching directions. Golden section method and quadratic fit-sectioning method are tested for one dimensional search. Objective function is defined as a ratio of generation rate of the turbulent kinetic energy to pressure head. Sweep angle distributions are used as design variables.

• Proceedings of the KIEE Conference
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• 2003.07d
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• pp.2176-2178
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• 2003

This paper presents the intelligent modeling method of chaotic systems using a DNA coding based wavelet neural network(WNN). Generally the mathematical teaming method such as gradient descent method is used to adjust the parameters of WNN, which has much computational cost. To overcome this kind of problem, we use the DNA coding method as the learning method of WNN, and then combine it with the WNN. Finally, to verify the efficiency of our method, we apply the proposed DNA coding based wavelet neural network for modeling of Duffing system, which is a representative continuous-time chaotic system.

• The Transactions of the Korea Information Processing Society
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• v.6 no.12
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• pp.3703-3709
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• 1999

We propose a new approach to reconstruct the surface shape of an object from a shaded image. We use genetic algorithm instead of gradient descent algorithm which is apt to take to local minima and also proposes genetic representation and suitable genetic operators for manipulating 2-D image. And for more effective execution, we suggest hierarchical process to reconstruct minutely the surface of an object after coarse and global reconstruction. A modified Lambertian illumination model including the distance factor was herein adopted to get more reasonable result and an experiment was performed with synthesized and real images to demonstrate the devised method, of which results show the usefulness of our method.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.33B no.4
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• pp.201-208
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• 1996

This paper proposes an efficient method for improving the training performance of the neural network using a hybrid of backpropagation algorithm and dynamic tunneling system.The backpropagation algorithm, which is the fast gradient descent method, is applied for high-speed optimization. The dynamic tunneling system, which is the deterministic method iwth a tunneling phenomenone, is applied for blobal optimization. Converging to the local minima by using the backpropagation algorithm, the approximate initial point for escaping the local minima is estimated by the pattern classification, and the simulation results show that the performance of proposed method is superior th that of backpropagation algorithm with randomized initial point settings.

• 제어로봇시스템학회:학술대회논문집
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• 1999.10a
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• pp.173-176
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• 1999

This paper shows a self tuning fuzzy inference method by the genetic algorithm in the fuzzy-sliding mode control for a Polishing robot. Using this method, the number of inference rules and the shape of membership functions are determined by the genetic algorithm. The fuzzy outputs of the consequent part are derived by the gradient descent method. Also, it is guaranteed that .the selected solution become the global optimal solution by optimizing the Akaike's information criterion expressing the quality of the inference rules. It is shown by simulations that the method of fuzzy inference by the genetic algorithm provides better learning capability than the trial and error method.