Optimal matrix approximants in structural identification
Journal of Optimization Theory and Applications
Algorithms of Nondifferentiable Optimization: Development and Application
Cybernetics and Systems Analysis
A Dual Approach to Semidefinite Least-Squares Problems
SIAM Journal on Matrix Analysis and Applications
Least-Squares Covariance Matrix Adjustment
SIAM Journal on Matrix Analysis and Applications
The nearness problems for symmetric matrix with a submatrix constraint
Journal of Computational and Applied Mathematics
A generalized inverse eigenvalue problem in structural dynamic model updating
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
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The problem of finding the least change adjustment to a stiffness matrix modeled by finite element method is considered in this paper. Desired stiffness matrix properties such as symmetry, sparsity, positive semidefiniteness, and satisfaction of the characteristic equation are imposed as side constraints of the constructed optimal matrix approximation for updating the stiffness matrix, which matches measured data better. The dual problems of the original constrained minimization are presented and solved by subgradient algorithms with different line search strategies. Some numerical results are included to illustrate the performance and application of the proposed methods.