New computer methods for global optimization
New computer methods for global optimization
The enclosure of solutions of parameter-dependent systems of equations
Reliability in computing: the role of interval methods in scientific computing
Simulated annealing and Boltzmann machines: a stochastic approach to combinatorial optimization and neural computing
Adaptation in natural and artificial systems
Adaptation in natural and artificial systems
An interval algorithm for constrained global optimization
ICCAM'92 Proceedings of the fifth international conference on Computational and applied mathematics
Genetic Algorithms in Search, Optimization and Machine Learning
Genetic Algorithms in Search, Optimization and Machine Learning
Simulated Annealing: Searching for an Optimal Temperature Schedule
SIAM Journal on Optimization
A Trust-Region Approach to Nonlinear Systems of Equalities and Inequalities
SIAM Journal on Optimization
Heuristic search and pruning in polynomial constraints satisfaction
Annals of Mathematics and Artificial Intelligence
A hybrid global optimization method: the one-dimensional case
Journal of Computational and Applied Mathematics
Numerical solution for bounding feasible point sets
Journal of Computational and Applied Mathematics
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
Computational Optimization and Applications
Study of multiscale global optimization based on parameter space partition
Journal of Global Optimization
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We extend the hybrid global optimization method proposed by Xu (J. Comput. Appl. Math. 147 (2002) 301-314) 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.