Journal
ENGINEERING OPTIMIZATION
Volume 50, Issue 5, Pages 781-796Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/0305215X.2017.1355367
Keywords
Interior-point methods; primal-dual methods; quadratic programming; initial guesses; preconditioning
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The particularities of the aircraft parts riveting process simulation necessitate the solution of a large amount of contact problems. A primal-dual interior-point method-based solver is proposed for solving such problems efficiently. The proposed method features a worst case polynomial complexity bound O(root n ln c(-1)) on the number of iterations, where n is the dimension of the problem and epsilon is a threshold related to desired accuracy. In practice, the convergence is often faster than this worst case bound, which makes the method applicable to large-scale problems. The computational challenge is solving the system of linear equations because the associated matrix is ill conditioned. To that end, the authors introduce a preconditioner and a strategy for determining effective initial guesses based on the physics of the problem. Numerical results are compared with ones obtained using the Goldfarb-Idnani algorithm. The results demonstrate the efficiency of the proposed method.
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