# A Trust Region Method for Optimization Problem with Singular Solutions

A Trust Region Method for Optimization Problem with Singular Solutions 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

# A Trust Region Method for Optimization Problem with Singular Solutions

, Volume 56 (3) – Dec 1, 2007
16 pages

/lp/springer_journal/a-trust-region-method-for-optimization-problem-with-singular-solutions-3dStICuHGm
Publisher
Springer-Verlag
Subject
Mathematics; Numerical and Computational Methods ; Mathematical Methods in Physics; Mathematical and Computational Physics; Systems Theory, Control; Calculus of Variations and Optimal Control; Optimization
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s00245-007-9009-6
Publisher site
See Article on Publisher Site

### 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.

### Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Dec 1, 2007

### References

• CUTE: constrained and unconstrained testing environment
Bongartz, I.; Conn, A.R.; Gould, N.I.M.; Toint, Ph.L.

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