On the Convergence of a Trust-Region Method for Solving Constrained Nonlinear Equations with Degenerate Solutions

X. J. Tong and L. Qi
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X. J. Tong: Changsha University of Science and Technology
L. Qi: Hong Kong Polytechnic University

Journal of Optimization Theory and Applications, 2004, vol. 123, issue 1, No 9, 187-211

Abstract: Abstract This paper presents a trust-region method for solving the constrained nonlinear equation F(x) = 0, x ∈ Ω, where Ω ⊂ R n is a nonempty and closed convex set, F is defined on the open set containing Ω and is continuously differentiable. The iterates generated by the method are feasible. The method is globally and quadratically convergent under local error bounded assumption on F. The results obtained are extensions of the work of Yamashita Fukushima (Ref. 1) and Fan Yuan (Ref. 2) for unconstrained nonlinear equations. Numerical results show that the new algorithm works quite well.

Keywords: Constrained nonlinear equations; trust-region methods; global convergence; superlinear/quadratic convergence; error bound (search for similar items in EconPapers)
Date: 2004
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Citations: View citations in EconPapers (5)

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DOI: 10.1023/B:JOTA.0000043997.42194.dc

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