Matrix linear variational inequality approach for finite element model updating

Yuan, Qiaoxia

doi:10.1016/j.ymssp.2011.09.016

Cited by 5 publications

(3 citation statements)

References 32 publications

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“…Optimization problems on the space of matrices, which are restricted to the convex set of positive definite matrices, arise in various applications, such as statistics, as well as financial mathematics, model updating, and in general in matrix least-squares settings (see e.g., Boyd and Xiao 2005;Escalante and Raydan 1996;Fletcher 1985;Higham 2002;Hu and Olkin 1991;Yuan 2012). …”

Section: A Matrix Problem On the Set Of Positive Definite Matricesmentioning

confidence: 99%

Spectral Projected Gradient Methods: Review and Perspectives

Birgin¹,

Martínez²,

Raydan³

2014

J. Stat. Soft.

142

112

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Over the last two decades, it has been observed that using the gradient vector as a search direction in large-scale optimization may lead to efficient algorithms. The effectiveness relies on choosing the step lengths according to novel ideas that are related to the spectrum of the underlying local Hessian rather than related to the standard decrease in the objective function. A review of these so-called spectral projected gradient methods for convex constrained optimization is presented. To illustrate the performance of these low-cost schemes, an optimization problem on the set of positive definite matrices is described.

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Section: A Matrix Problem On the Set Of Positive Definite Matricesmentioning

confidence: 99%

Spectral Projected Gradient Methods: Review and Perspectives

Birgin¹,

Martínez²,

Raydan³

2014

J. Stat. Soft.

142

112

View full text Add to dashboard Cite

show abstract

“…However, these methods fail to guarantee that the updated stiffness or mass matrices are positive semidefinite. Recently, Yuan [30][31][32] considered the problem of updating the analytical stiffness matrix to satisfy simultaneously the dynamic equation, symmetry, positive semidefiniteness, and sparsity and proposed a matrix linear variational inequality approach and proximal-point method for solving the problem using a partial Lagrangian multiplier technique.…”

Section: Introductionmentioning

confidence: 99%

The matrix pencil nearness problem in structural dynamic model updating

Yuan

Dai

2015

J Eng Math

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This paper considers the problem of finding the least change adjustment to a given matrix pencil. The desired matrix properties, including satisfaction of the characteristic equation, symmetry, positive semidefiniteness, and sparsity, are imposed as side constraints to form the optimal matrix pencil approximation problem. This problem is related to the frequently encountered engineering problem of a structural modification to the dynamic behavior of a structure. Conditions ensuring the feasible region of the matrix pencil nearness problem are analyzed using a matrix decomposition technique. An unconstrained minimization formulation is presented in terms of the Lagrangian multiplier method and solved by a subgradient algorithm. Numerical results are included to illustrate the performance and application of the proposed method.

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“…Most of the existed methods just take part of the positive semidefiniteness and the sparsity requirement of the updated matrix into consideration. Recently, Yuan [30,31] considered the problem of updating the analytical stiffness matrix to satisfy with the dynamic equation, symmetry, positive semidefiniteness and sparsity simultaneously, proposed the matrix linear variational inequality approach and proximal-point method for solving the problem by using partial Lagrangian multipliers technique. In this paper, both the mass and stiffness matrices are updated to satisfy with the dynamic equation, symmetry, positive semidefiniteness and sparsity simultaneously.…”

Section: Introductionmentioning

confidence: 99%

Matrix linear variational inequality approach for finite element model updating

Cited by 5 publications

References 32 publications

Spectral Projected Gradient Methods: Review and Perspectives

Spectral Projected Gradient Methods: Review and Perspectives

The matrix pencil nearness problem in structural dynamic model updating

Optimal matrix pencil approximation problem in structural dynamic model updating

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