New computer methods for global optimization
New computer methods for global optimization
Spacefilling curves and the planar travelling salesman problem
Journal of the ACM (JACM)
Lipschitzian optimization without the Lipschitz constant
Journal of Optimization Theory and Applications
Global one-dimensional optimization using smooth auxiliary functions
Mathematical Programming: Series A and B
SIAM Journal on Optimization
Stochastic Global Optimization: Problem Classes and Solution Techniques
Journal of Global Optimization
A Locally-Biased form of the DIRECT Algorithm
Journal of Global Optimization
Modifications of the direct algorithm
Modifications of the direct algorithm
ACM Transactions on Mathematical Software (TOMS)
On the multilevel structure of global optimization problems
Computational Optimization and Applications
Global Search Based on Efficient Diagonal Partitions and a Set of Lipschitz Constants
SIAM Journal on Optimization
Global Optimization with Non-Convex Constraints - Sequential and Parallel Algorithms (Nonconvex Optimization and its Applications Volume 45) (Nonconvex Optimization and Its Applications)
A new class of test functions for global optimization
Journal of Global Optimization
Parallel scalable algorithms with mixed local-global strategy for global optimization problems
MTPP'10 Proceedings of the Second Russia-Taiwan conference on Methods and tools of parallel programming multicomputers
Global optimization using dimensional jumping and fuzzy adaptive simulated annealing
Applied Soft Computing
Lipschitz gradients for global optimization in a one-point-based partitioning scheme
Journal of Computational and Applied Mathematics
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In this paper, the global optimization problem min"y"@?"SF(y) with S=[a,b], a,b@?R^N, and F(y) satisfying the Lipschitz condition, is considered. To deal with it four algorithms are proposed. All of them use numerical approximations of space-filling curves to reduce the original Lipschitz multi-dimensional problem to a univariate one satisfying the Holder condition. The Lipschitz constant is adaptively estimated by the introduced methods during the search. Local tuning on the behavior of the objective function and a newly proposed technique, named local improvement, are used in order to accelerate the search. Convergence conditions are given. A theoretical relation between the order of a Hilbert space-filling curve approximation used to reduce the problem dimension and the accuracy of the resulting solution is established, as well. Numerical experiments carried out on several hundreds of test functions show a quite promising performance of the new algorithms.