Convergence analysis of the direct algorithm

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Adaptive Sensitive Reweighting to Mitigate Bias in Fairness-aware Classification (2018, methodology): “Hence, to optimize CULEP parameters, we employ the DIvided RECTangles (DIRECT) method [14, 15, 23], which is guaranteed to yield globally optimal solutions in Lipschitz-continuous objective spaces.”
Efficient Multi-Start Strategies for Local Search Algorithms (2009, methodology): “The selection mechanism is analogous to the DIRECT algorithm [15,8,14] for optimizing Lipschitz-functions with an unknown constant, where preference is given to rectangles that may contain the global optimum.”
Self-verifying variational quantum simulation of lattice models (2018, methodology): “We now address questions related to the complexity and scalability 10,18,29,51,56,57 of the VQS algorithm we employ, applied to the specific example of Schwinger model ground states simulated with trapped ions.”
Mesh Adaptive Direct Search Algorithms for Constrained Optimization (2006, methodology): “The reader will find a quite different algorithm analyzed using the same concepts in [15].”
From Bandits to Monte-Carlo Tree Search: The Optimistic Principle Applied to Optimization and Planning (2014, background): “Thus we are able to derive finite-time loss bounds in a much broader setting than the setting of DIRECT, for which, and to the best of our knowledge, there is no finite-time analysis (only the consistency property limn→∞ rn = 0 is proven in [Finkel and Kelley, 2004]).”