Approximation and optimization on the Wiener space
Journal of Complexity
The complexity of computation of the global extremum in a class of multi-extremum problems
USSR Computational Mathematics and Mathematical Physics
Lipschitzian optimization without the Lipschitz constant
Journal of Optimization Theory and Applications
The real number model in numerical analysis
Journal of Complexity
Lower bound on complexity of optimization of continuous functions
Journal of Complexity
Efficient Multi-start Strategies for Local Search Algorithms
ECML PKDD '09 Proceedings of the European Conference on Machine Learning and Knowledge Discovery in Databases: Part I
Lipschitz bandits without the Lipschitz constant
ALT'11 Proceedings of the 22nd international conference on Algorithmic learning theory
Efficient multi-start strategies for local search algorithms
Journal of Artificial Intelligence Research
Lipschitz condition for finding real roots of a vector function
Journal of Computational Methods in Sciences and Engineering
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We consider the global optimization problem for d-variate Lipschitz functions which, in a certain sense, do not increase too slowly in a neighborhood of the global minimizer(s). On these functions, we apply optimization algorithms which use only function values. We propose two adaptive deterministic methods. The first one applies in a situation when the Lipschitz constant L is known. The second one applies if L is unknown. We show that for an optimal method, adaptiveness is necessary and that randomization (Monte Carlo) yields no further advantage. Both algorithms presented have the optimal rate of convergence.