• Title/Summary/Keyword: Unconstrained optimization

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Length Optimization for Unconstrained Visco-elastic Damping Layer of Beams (비구속형 점탄성 제진층을 갖는 보의 제진층 길이 최적화)

  • Lee, Doo-Ho;Hwang, Woo-Seok
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.13 no.12
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    • pp.938-946
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    • 2003
  • Length of an unconstrained viscoelastic damping layer on beams is determined to maximizeloss factor using a numerical search method. The fractional derivative model can describe damping characteristics of viscoelastic damping materials accurately, and is used to represent nonlinearity of complex modulus with frequencies and temperatures. Equivalent flexural rigidity of the unconstrained beam is obtained using Ross, Ungar, Kelvin[RUK] equation. The loss factors of partially covered unconstrained beam are calculated by a modal strain energy method. Optimal lengths of the unconstrained viscoelastic damping layer of beams are identified with ambient temperatures and thickness ratios of beam and damping layer by using a finite-difference-based steepest descent method.

Length Optimization for Unconstrained Visco-elastic Damping Layer of Beams (비구속형 점탄성 제진층을 갖는 보의 제진층 길이 최적화)

  • 이두호;황우석
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • pp.665-671
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    • 2003
  • Length of an unconstrained viscoelastic damping layer on beams is determined to maximize loss factor using a numerical search method. The fractional derivative model can describe damping characteristics of the viscoelastic damping material, and is used to represent nonlinearity of complex modulus with frequencies and temperatures. Equivalent flexural rigidity of the unconstrained beam is obtained using Ross, Ungar, Kerwin(RUK) equation. The loss factors of partially covered unconstrained beam are calculated by a modal strain energy method. Optimal lengths of the unconstrained viscoelastic damping layer of beams are obtained with respect to ambient temperatures and thickness ratios of beam and damping layer.

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Optimal Treatment of Unconstrained Visco-elastic Damping Layer on Beam to Minimize Vibration Responses (동적응답을 최소화하는 비구속형 제진보의 제진부위 최적설계)

  • Lee, Doo-Ho
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • pp.656-661
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    • 2005
  • An optimization formulation of unconstrained damping treatment on beams is proposed to minimize vibration responses using a numerical search method. The fractional derivative model is combined with RUK's equivalent stiffness approach in order to represent nonlinearity of complex modulus of damping materials with frequency and temperature. The loss factors of partially covered unconstrained beam are calculated by the modal strain energy method. Vibration responses are calculated by using the modal superposition method, and of which design sensitivity formula with respect to damping layout is derived analytically. Plugging the sensitivity formula into optimization software, we can determine optimally damping treatment region that gives minimum forced response under a given boundary condition. A numerical example shows that the proposed method is very effective in minimizing vibration responses with unconstrained damping layer treatment.

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A NOVEL FILLED FUNCTION METHOD FOR GLOBAL OPTIMIZATION

  • Lin, Youjiang;Yang, Yongjian;Zhang, Liansheng
    • Journal of the Korean Mathematical Society
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    • v.47 no.6
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    • pp.1253-1267
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    • 2010
  • This paper considers the unconstrained global optimization with the revised filled function methods. The minimization sequence could leave from a local minimizer to a better minimizer of the objective function through minimizing an auxiliary function constructed at the local minimizer. Some promising numerical results are also included.

MODIFIED LIMITED MEMORY BFGS METHOD WITH NONMONOTONE LINE SEARCH FOR UNCONSTRAINED OPTIMIZATION

  • Yuan, Gonglin;Wei, Zengxin;Wu, Yanlin
    • 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.

THE PERFORMANCE OF A MODIFIED ARMIJO LINE SEARCH RULE IN BFGS OPTIMIZATION METHOD

  • Kim, MinSu;Kwon, SunJoo;Oh, SeYoung
    • 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.

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GLOBAL CONVERGENCE OF AN EFFICIENT HYBRID CONJUGATE GRADIENT METHOD FOR UNCONSTRAINED OPTIMIZATION

  • Liu, Jinkui;Du, Xianglin
    • Bulletin of the Korean Mathematical Society
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    • v.50 no.1
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    • pp.73-81
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    • 2013
  • In this paper, an efficient hybrid nonlinear conjugate gradient method is proposed to solve general unconstrained optimization problems on the basis of CD method [2] and DY method [5], which possess the following property: the sufficient descent property holds without any line search. Under the Wolfe line search conditions, we proved the global convergence of the hybrid method for general nonconvex functions. The numerical results show that the hybrid method is especially efficient for the given test problems, and it can be widely used in scientific and engineering computation.

New Parameterizations for Multi-Step Unconstrained Optimization

  • Moghrabi, I.A.;Kassar, A.N
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.3 no.1
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    • pp.71-79
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    • 1999
  • We consider multi-step quasi-Newton methods for unconstrained optimization. These methods were introduced by Ford and Moghrabi [1, 2], who showed how interpolating curves could be used to derive a generalization of the Secant Equation (the relation normally employed in the construction of quasi-Newton methods). One of the most successful of these multi-step methods makes use of the current approximation to the Hessian to determine the parameterization of the interpolating curve in the variable-space and, hence, the generalized updating formula. In this paper, we investigate new parameterization techniques to the approximate Hessian, in an attempt to determine a better Hessian approximation at each iteration and, thus, improve the numerical performance of such algorithms.

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CONVERGENCE OF THE NONMONOTONE PERRY-SHANNO METHOD FOR UNCONSTRAINED OPTIMIZATION

  • Ou, Yigui;Ma, Wei
    • Journal of applied mathematics & informatics
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    • v.30 no.5_6
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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.

GLOBAL CONVERGENCE OF A NEW SPECTRAL PRP CONJUGATE GRADIENT METHOD

  • Liu, Jinkui
    • Journal of applied mathematics & informatics
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    • v.29 no.5_6
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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.