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Projected quasi-Newton algorithm with trust region for constrained optimization (1990)

Zhang, J. Z. ; Zhu, D. T.

Springer

Journal of optimization theory and applications 67 (1990), S. 369-393

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ISSN: 1573-2878

Keywords: Two-sided projected Hessians ; trust regions ; differentiable penalty functions ; global convergence ; two-step Q-superlinear rate ; constrained optimization

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract In Ref. 1, Nocedal and Overton proposed a two-sided projected Hessian updating technique for equality constrained optimization problems. Although local two-step Q-superlinear rate was proved, its global convergence is not assured. In this paper, we suggest a trust-region-type, two-sided, projected quasi-Newton method, which preserves the local two-step superlinear convergence of the original algorithm and also ensures global convergence. The subproblem that we propose is as simple as the one often used when solving unconstrained optimization problems by trust-region strategies and therefore is easy to implement.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF00940481

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Numerical modelling of crack propagation using multi-variable and breakable finite elements (1990)

Zhang, J. Y. ; Hsu, T. R. ; Wang, I. Q.

New York, NY [u.a.] : Wiley-Blackwell

Communications in Applied Numerical Methods 6 (1990), S. 215-222

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ISSN: 0748-8025

Keywords: Engineering ; Engineering General

Source: Wiley InterScience Backfile Collection 1832-2000

Topics: Mathematics , Technology

Notes: In this study, the advantage of the multi-variable finite-element model based on the generalized virtual work principle is described. The model has been applied to the elasto-plastic fracture analysis with finite deformations. Using the multi-variable finite-element model with a‘breakable finite-element’ concept, the authors proposed an algorithm which can more accurately simulate the crack growth. Numerical examples illustrate that the algorithm presented can be successfully used to predict whether the crack growth is stable or unstable. The rupture effective strain is considered as a fracture criterion, and some comparisons between various criteria are also provided.

Additional Material: 5 Ill.