• Journal of the Korean Mathematical Society
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• v.47 no.4
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• pp.767-788
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• 2010

In this paper, we propose two limited memory BFGS algorithms with a nonmonotone line search technique for unconstrained optimization problems. The global convergence of the given methods will be established under suitable conditions. Numerical results show that the presented algorithms are more competitive than the normal BFGS method.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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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.

• 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.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.12 no.1
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• pp.197-205
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• 1992

For the optimal design of composite breakwaters, a computer program PROCOBRA is developed using the combined ALM-BFGS algorithm. A model formulation for the section design optimization problem of composite breakwaters is proposed where a concept of subsectional weighting factors is introduced in the objective function. Usability of the program is verified through a numerical example. From the study, it is found that the ALM-BFGS method is reliable and can be effectively applied for the design optimization of coastal structures. Compared with conventional design process, it is proved that the economical design of composite breakwaters is possible.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.195-205
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• 2004

To the unconstrained programme of non-convex function, this article give a modified BFGS algorithm. The idea of the algorithm is to modify the approximate Hessian matrix for obtaining the descent direction and guaranteeing the efficacious of the quasi-Newton iteration pattern. We prove the global convergence properties of the algorithm associating with the general form of line search, and prove the quadratic convergence rate of the algorithm under some conditions.

• Bulletin of the Society of Naval Architects of Korea
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• v.23 no.3
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• pp.39-44
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• 1986

The basic BFGS procedure for the nonlinear finite element analysis is reviewed. Through a simple numerical example, promising characteristics of the method evaluated discussed. Based on the discussion of computational performance, a modified BFGS algorithm with substructuring is derived and proposed for the quasi-static analysis of large-scale nonlinear structures.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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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 the Chungcheong Mathematical Society
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• v.21 no.1
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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.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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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.

• The Journal of the Acoustical Society of Korea
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• v.19 no.1
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• pp.25-31
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• 2000

In this paper, we proposed an algorithm that used a direct method to set an initial value of Broydon-Fletcher-Goldfarb-Shanno(BFGS) method and, accordingly, conducted an experiment in optimal directivity synthesis of adaptive ultrasonic transducer by point source array. To certify the efficiency of this method, quasi-ideal beam with arbitrary beam width, rotating beam, and multi beam, all with the limited side lobe level -30dB, were chosen to check the problem of directivity synthesis that was formed by point source array in the second dimensional sound field. The numerical calculation results showed that the proposed method performed the directivity synthesis faster than the BFGS method did. In addition, the proposed method showed a good error correction for directivity synthesis, and did not demand the choice of initial value. Finally, it is also shown that the proposed method can be used for the adaptive control that was not possible with the direct method alone.