• Title/Summary/Keyword: BFGS Quasi-Newton optimization method

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Displacement-based Seismic Assessment and Rehabilitation of Asymmetric Wall Structures (비대칭 벽식 구조지 변위기초 내진성능평가 및 보강)

  • Hong, Sung-Gul;Ha, Tae-Hyu
    • Journal of the Earthquake Engineering Society of Korea
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    • v.9 no.3 s.43
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    • pp.23-32
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    • 2005
  • Torsional behavior of eccentric structure under seismic leading may cause the stress and/or deformation concentration, which arouse the failure of the structure in an unexpected manner. This study suggests D-R relationship which shows the overall displacement and rotation of the system based on the ultimate displacement capacity of the each lateral load resistant member. Using the suggested D-R relationship and displacement spectrum, the seismic assessment is conducted and verified in comparison with the time history analysis result. Multi-level seismic assessment Is considered which takes multiple seismic hazard levels and respective performance levels into account. Finally, based on the seismic assessment result, seismic rehabilitation process is presented. In this research, two rehabilitation methods are considered. One is done by means of stiffening/strengthening the seismic resistant members, and the other is based on the member ductility. Especially, in the first method, to optimize the rehabilitation result, the rehabilitation problem is modeled as an optimization problem, and solved using BFGS quasi-Newton optimization method.

A TYPE OF MODIFIED BFGS ALGORITHM WITH ANY RANK DEFECTS AND THE LOCAL Q-SUPERLINEAR CONVERGENCE PROPERTIES

  • Ge Ren-Dong;Xia Zun-Quan;Qiang Guo
    • 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.

SCALING METHODS FOR QUASI-NEWTON METHODS

  • MOGHRABI, ISSAM A.R.
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.6 no.1
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    • pp.91-107
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    • 2002
  • This paper presents two new self-scaling variable-metric algorithms. The first is based on a known two-parameter family of rank-two updating formulae, the second employs an initial scaling of the estimated inverse Hessian which modifies the first self-scaling algorithm. The algorithms are compared with similar published algorithms, notably those due to Oren, Shanno and Phua, Biggs and with BFGS (the best known quasi-Newton method). The best of these new and published algorithms are also modified to employ inexact line searches with marginal effect. The new algorithms are superior, especially as the problem dimension increases.

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