• Journal of applied mathematics & informatics
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• 제22권1_2호
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• pp.193-208
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• 2006

A modified BFGS algorithm for solving the unconstrained optimization, whose Hessian matrix at the minimum point of the convex function is of rank defects, is presented in this paper. The main idea of the algorithm is first to add a modified term to the convex function for obtain an equivalent model, then simply the model to get the modified BFGS algorithm. The superlinear convergence property of the algorithm is proved in this paper. To compared with the Tensor algorithms presented by R. B. Schnabel (seing [4],[5]), this method is more efficient for solving singular unconstrained optimization in computing amount and complication.

• Journal of applied mathematics & informatics
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• 제30권5_6호
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• pp.759-772
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• 2012

In this paper, semi-infinite constrained programming, a class of constrained nonsmooth optimization problems, are transformed into unconstrained nonsmooth convex programs under the help of exact penalty function. The unconstrained objective function which owns the primal-dual gradient structure has connection with $\mathcal{VU}$-space decomposition. Then a $\mathcal{VU}$-space decomposition method can be applied for solving this unconstrained programs. Finally, the superlinear convergence algorithm is proved under certain assumption.

• Journal of applied mathematics & informatics
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• 제24권1_2호
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• pp.325-331
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• 2007

To the unconstrained programme of non-convex function, this article give a modified BFGS algorithm associated with the general line search model. The idea of the algorithm is to modify the approximate Hessian matrix for obtaining the descent direction and guaranteeing the efficacious of the new quasi-Newton iteration equation $B_{k+1}s_k=y^*_k,\;where\;y^*_k$ is the sum of $y_k\;and\;A_ks_k,\;and\;A_k$ is some matrix. The global convergence properties of the algorithm associating with the general form of line search is proved.

• Journal of the Korea Safety Management & Science
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• 제11권3호
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• pp.209-216
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• 2009

A development in method of evaluating the measurement precisions using approximate F tests and variance components from expected mean square (EMS) is investigated. The research proposes three-factor mixed measurement models with the fixed and random factors. Unrestricted and unconstrained design work was rarely studied, while restricted and constrained designs have been significantly discussed. The unrestricted and unconstrained designs assume to be an independence of interaction. The proposed evaluation method about the measurement precisions can be extended to four-factor random measurement model or mixed measurement model. The study also presents the three evaluation indexes of precisions such as R&RTR (Reproducibility & Repeatability-To-Total Precision Ratio), PTR (Precision-To-Tolerance Ratio), and SNR (Signal-To-Noise Ratio). Numerical examples are proposed to evaluate the approximate F tests with Satterthwaite degrees of freedom and three indexes using the measurement precisions from EMS.

• Journal of the Korea Safety Management & Science
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• 제11권3호
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• pp.73-78
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• 2009

In this paper, we developed the care system for older people living alone using the RFID technologies and the living informations. The care system store living informations, extracted through a unconstrained detection method by the RFID tags and readers, into a monitering server. The unconstrained detection method improved a weakness of existing systems that detected a living informations through an infrared sensor, ultrasonic sensor, camera, consumed quantity of the tap water or gas. The result of this study will playa very important role, as a part of a composite older-welfare services. Also, in the future, accumulated living informations will be allowed for a health data of older peoples.

• Journal of the Institute of Convergence Signal Processing
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• 제3권1호
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• pp.48-53
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• 2002

In this paper, we presented a new approach to the recognition of unconstrained handwritten numerals using an improved RBF(Radial Basis Function) Neural Networks. The RBF Neural Networks used Raised Cosine as a basis function to improve discrimination and reduce processing time. The performance of Raised Cosine RBF Neural Networks classifier was evaluated using totally unconstrained handwritten numeral database of Concordia University, Montreal, Canada, and the experimental results showed the recognition rate of 98.05%.

• Nonlinear Functional Analysis and Applications
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• 제26권4호
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• pp.811-837
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• 2021

In this paper, we propose a new conjugate gradient method for solving unconstrained optimization models. By using exact and strong Wolfe line searches, the proposed method possesses the sufficient descent condition and global convergence properties. Numerical results show that the proposed method is efficient at small, medium, and large dimensions for the given test functions. In addition, the proposed method was applied to solve practical application problems in portfolio selection.

• Journal of applied mathematics & informatics
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• 제17권1_2_3호
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• pp.401-418
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• 2005

In this paper, a dual algorithm, based on a smoothing function of Bertsekas (1982), is established for solving unconstrained minimax problems. It is proven that a sequence of points, generated by solving a sequence of unconstrained minimizers of the smoothing function with changing parameter t, converges with Q-superlinear rate to a Kuhn-Thcker point locally under some mild conditions. The relationship between the condition number of the Hessian matrix of the smoothing function and the parameter is studied, which also validates the convergence theory. Finally the numerical results are reported to show the effectiveness of this algorithm.

• Journal of applied mathematics & informatics
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• 제29권5_6호
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• pp.1303-1309
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• 2011

Based on the PRP method, a new spectral PRP conjugate gradient method has been proposed to solve general unconstrained optimization problems which produce sufficient descent search direction at every iteration without any line search. Under the Wolfe line search, we prove the global convergence of the new method for general nonconvex functions. The numerical results show that the new method is efficient for the given test problems.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 한국경영과학회 2007년도 추계학술대회 및 정기총회
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• pp.309-312
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• 2007

We consider a proportionate flow shop problem with controllable processing times. The objective is to minimize the sum of total completion time and total compression cost, in which the cost function of compressing the processing times is non-decreasing concave. We show that the problem can be solved in polynomial time by reducing it to a polynomially solvable 0-1 unconstrained quadratic program.