• Journal of applied mathematics & informatics
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• 제22권1_2호
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• pp.461-466
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• 2006

In this paper, an algorithm with a new Armijo-type line search is proposed that ensure global convergence of a correlative Polak-Ribiere conjugate method for the unconstrained minimization of non-convex differentiable function.

• Kyungpook Mathematical Journal
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• 제64권1호
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• pp.95-111
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• 2024

The filled function method is useful in solving unconstrained global optimization problems. However, depending on the type of function, and parameters used, there are limitations that cause difficultiies in implemenations. Exponential and logarithmic functions lead to the overflow effect, requiring iterative adjustment of the parameters. This paper proposes a polynomial-filled function that has a general form, is non-exponential, nonlogarithmic, non-parameteric, and continuously differentiable. With this newly proposed filled function, the aforementioned shortcomings of the filled function method can be overcome. To confirm the superiority of the proposed filled function algorithm, we apply it to a set of unconstrained global optimization problems. The data derived by numerical implementation shows that the proposed filled function can be used as an alternative algorithm when solving unconstrained global optimization problems.

• Journal of applied mathematics & informatics
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• 제30권5_6호
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• pp.971-980
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• 2012

In this paper, a method associating with one new form of nonmonotone linesearch technique is proposed, which can be regarded as a generalization of the Perry-Shanno memoryless quasi-Newton type method. Under some reasonable conditions, the global convergence of the proposed method is proven. Numerical tests show its efficiency.

• Journal of applied mathematics & informatics
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• 제23권1_2호
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• pp.311-319
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• 2007

This article studies a modified BFGS algorithm for solving smooth unconstrained strongly convex minimization problem. The modified BFGS method is based on the new quasi-Newton equation $B_k+1{^s}_k=yk\;where\;y_k^*=yk+A_ks_k\;and\;A_k$ is a matrix. Wei, Li and Qi [WLQ] have proven that the average performance of two of those algorithms is better than that of the classical one. In this paper, we prove the global convergence of these algorithms associated to a general line search rule.

• 센서학회지
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• 제20권2호
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• pp.118-123
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• 2011

Heart related diseases mainly caused by heavy work load and increasing stress in human daily life. Therefore, researches on mobile healthcare monitoring for daily life has been carried out. Notably, wearable healthcare monitoring system which has least restriction has been tried to provide an emergency alert of abnormal heart rate. In this study, we developed chair type unconstrained BCG measurement system which able to perform continuous heart status monitoring at the office and daily life in the unconstrained way. Furthermore, adaptive threshold is used to detect the heart rate from BCG signals. The HRV(heart rate variability) is calculated from heart rate interval. ECG signal measured using conventional method and BCG signal measured using unconstraint system are carried out simultaneously for the purpose of performance evaluation. From the comparison result, BCG signal shows a similar heart beat characteristic as ECG signal. This proves the possibility of practical implementation of unconstraint healthcare monitoring system. In addition, medical examination like valsalva maneuver is performed to observe the changes in HRV due to stress. By performing valsalva maneuver, heart is said to be placed under an artificial physical stress condition. Under this artificial physical stress condition, the time and frequency domain of HRV parameters are evaluated.

• 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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• 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.

• 대한족부족관절학회지
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• 제11권2호
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• pp.177-181
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• 2007

Purpose: The purpose of this study is to compare the two prosthesis that used for total ankle arthroplasty. Materials and Methods: From Sept. 2003 to Jun 2006, 13 patients and 14 ankles that could be follow up more than 1 months. Semiconstrained type (Group I, 7 cases) and Unconstrained type (Group II, 7 cases) were used for total ankle arthroplasty. Mean age was 63.2 year-old, 12 ankles are men and 2 ankles were women. Mean follow up periods were 29 months. The criteria to compare the clinical result were postoperative range of motion, AOFAS score and residual bone stock of medial malleolus. Results: Postoperative range of motion of group I was $43.6{\pm}9.4$ degrees and of group II was $50.7{\pm}7.3$ degrees (p=0.115). Postoperative AOFAS score of group I was $77.1{\pm}13.0$ points and of group II was $86.0{\pm}5.7$ points (p=0.094). Resected bone stock in medial malleolus of group I was $10.7{\pm}2.5\;mm$ and of group II was $5.1{\pm}1.2\;mm$ (p=0.003). Total number of complication in our study was 9 cases. 3 cases were a malleolar fracture, two occurred at intra-operation, the other at follow-up period. Re-operation was done in 6 cases, 3 cases were calcaneal corrective osteotomy, 2 cases were resection of a heterotopic bone and one case was pedicular flap operation for skin problem. Conclusion: In our hospital, mobile bearing type prosthesis shows good result than a semiconstrained type in respect of residual bone stock in medial malleolus. Postoperative range of motion and AOFAS score between two groups shows no significant difference. But small number of patients and short term follow up period is a defect in our study, afterward more population and long term follow up period are needed.

• 충청수학회지
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• 제21권1호
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• pp.117-127
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• 2008

The performance of a modified Armijo line search rule related to BFGS gradient type method with the results from other well-known line search rules are compared as well as analyzed. Although the modified Armijo rule does require as much computational cost as the other rules, it shows more efficient in finding local minima of unconstrained optimization problems. The sensitivity of the parameters used in the line search rules is also analyzed. The results obtained by implementing algorithms in Matlab for the test problems in [3] are presented.

• International Journal of Air-Conditioning and Refrigeration
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• 제13권2호
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• pp.71-82
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• 2005

The shape of $7\times7$ pin-fins heat sink is optimized numerically to obtain the minimum pressure drop and thermal resistance. In this study, the fin height (h), fin width (w), and fan-to-heat sink distance (c) are chosen as the design variables and the pressure drop $({\Delta}P)$ and thermal resistance $(\theta_j)$ are adopted as the objective functions. To obtain the optimum design values, we used the finite volume method for calculating the objective functions, the BFGS method for solving the unconstrained non-linear optimization problem, and the weighting method for predicting the multi-objective problem. The results show that the optimum design variables for the weighting coefficient of 0.5 are as follows: W=4.653 mm, h=59.215mm, and c=2.667mm. The objective functions corresponding to the optimal design are calculated as ${\Delta}P=6.82$ Pa and $(\theta_j)=0.56K/W$. The Pareto solutions are also presented for various weighting coefficients and they will offer very useful data to design the pin-fins heat sink.