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Zbl 1020.65033
Xu, Peiliang
A hybrid global optimization method: The multi-dimensional case. (English)
[J] J. Comput. Appl. Math. 155, No.2, 423-446 (2003). ISSN 0377-0427

Summary: We extend the hybrid global optimization method proposed by {\it P. Xu} [J. Comput. Appl. Math. 147, 301-314 (2002; Zbl 1013.65063)] for the one-dimensional case to the multi-dimensional case. The method consists of two basic components: local optimizers and feasible point finders. Local optimizers guarantee efficiency and speed of producing a local optimal solution in the neighbourhood of a feasible point. Feasible point finders provide the theoretical guarantee for the new method to always produce the global optimal solution(s) correctly. If a nonlinear nonconvex inverse problem has multiple global optimal solutions, our algorithm is capable of finding all of them correctly. Three synthetic examples, which have failed simulated annealing and genetic algorithms, are used to demonstrate the proposed method.

MSC 2000:: *65K05 Mathematical programming (numerical methods)
90C30 Nonlinear programming
90C53 Methods of quasi-Newton type

Keywords: nonlinear inverse problems; global optimization; feasible point finders; interval analysis; numerical examples; quasi-Newton method; algorithm

Citations: Zbl 1013.65063

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