Abstract
In this paper, we propose a trust region method for minimizing a function whose Hessian matrix at the solutions may be singular. The global convergence of the method is obtained under mild conditions. Moreover, we show that if the objective function is LC 2 function, the method possesses local superlinear convergence under the local error bound condition without the requirement of isolated nonsingular solution. This is the first regularized Newton method with trust region technique which possesses local superlinear (quadratic) convergence without the assumption that the Hessian of the objective function at the solution is nonsingular. Preliminary numerical experiments show the efficiency of the method.
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This work is partly supported by the National Natural Science Foundation of China (Grant Nos. 70302003, 10571106, 60503004, 70671100) and Science Foundation of Beijing Jiaotong University (2007RC014).
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Zhang, J., Wu, L. & Zhang, X. A Trust Region Method for Optimization Problem with Singular Solutions. Appl Math Optim 56, 379–394 (2007). https://doi.org/10.1007/s00245-007-9009-6
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DOI: https://doi.org/10.1007/s00245-007-9009-6