Performance Modeling and Analysis of a Massively Parallel Direct - Part 1
International Journal of High Performance Computing Applications
Lipschitz and Hölder global optimization using space-filling curves
Applied Numerical Mathematics
A partition-based global optimization algorithm
Journal of Global Optimization
Lipschitz gradients for global optimization in a one-point-based partitioning scheme
Journal of Computational and Applied Mathematics
Lipschitz global optimization methods in control problems
Automation and Remote Control
A modification of the DIRECT method for Lipschitz global optimization for a symmetric function
Journal of Global Optimization
Global search perspectives for multiobjective optimization
Journal of Global Optimization
Simplicial Lipschitz optimization without the Lipschitz constant
Journal of Global Optimization
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In the paper, the global optimization problem of a multidimensional "black-box" function satisfying the Lipschitz condition over a hyperinterval with an unknown Lipschitz constant is considered. A new efficient algorithm for solving this problem is presented. At each iteration of the method a number of possible Lipschitz constants are chosen from a set of values varying from zero to infinity. This idea is unified with an efficient diagonal partition strategy. A novel technique balancing usage of local and global information during partitioning is proposed. A new procedure for finding lower bounds of the objective function over hyperintervals is also considered. It is demonstrated by extensive numerical experiments performed on more than 1600 multidimensional test functions that the new algorithm shows a very promising performance.