Lipschitzian optimization without the Lipschitz constant

By Donald R. Jones, C. D. Perttunen, Bruce E. Stuckman. 1993

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Citations in the corpus

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.”
Taking the Human Out of the Loop: A Review of Bayesian Optimization (2016, methodology): “In practice, the community has resorted to using various techniques such as discretization [143] and adaptive grids [13], or similarly, the divided rectangles approach of [83], which was used in [28], [105], and [110].”
A Tutorial on Bayesian Optimization of Expensive Cost Functions, with Application to Active User Modeling and Hierarchical Reinforcement Learning (2010, methodology): “A particular advantage in active learning applications is that DIRECT can be implemented as an “any-time” algorithm, so that as long as the user is doing something else, it continues to optimize, and when interrupted, the program can use the best results found to that point in time.”
Learning Where to Attend with Deep Architectures for Image Tracking (2011, methodology): “We use DIRECT (Jones et al., 1993) due to the existence of a readily available implementation.”
Multi-fidelity Bayesian Optimisation with Continuous Approximations (2017, methodology): “Maximising ϕ t : We used the DiRect algorithm (Jones et al., 1993).”
Automated Machine Learning on Big Data using Stochastic Algorithm Tuning (2014, methodology): “We also tested covariance matrix adaptive evolution strategy (CMAES) [25] and dividing rectangles (DIRECT) [26] however found that these did not converge on this very noisy objective.”
Kriging is well-suited to parallelize optimization (2010, unknown): “A comparable approach called direct , although not based on OK, is described in [21]: the metamodel is piecewise linear and the uncertainty measure is a distance to already known points.”
Advanced Forward Modeling and Inversion of Stokes Profiles Resulting from the Joint Action of the Hanle and Zeeman Effects (2008, methodology): “When the observed structure is off the limb, imaging techniques can be used to esti- 9This proves to be fundamental to demonstrate that the global minimum will always be found (Jones et al. 1993). mate h.”
Automated configuration of algorithms for solving hard computational problems (2009, methodology): “(In experiments we omit due to their preliminary nature, we compared three methods for optimizing expected improvement inR17: random sampling, DIRECT (Jones et al., 1993), and CMA-ES (Hansen and Ostermeier, 1996).”
Optimal sizing study of hybrid wind/PV/diesel power generation unit (2011, methodology): “Many researchers have recently proved that the DIRECT algorithm, acronym for DIviding RECTangles and developed by Jones et al. (1993), is an effective deterministic algorithm to find the global optimum of several problems (Belfkira et al., 2008b) min x fiðxÞ i 2 ½1; n hkðxÞ ¼ 0 k 2 ½1; p gjðxÞ >¼ 0…”
Indistinguishable states I.: perfect model scenario (2001, background): “We find that simplex descent [22] and (branch and bound) global optimizations [12,14], do not work well, however, and may wander to a solution L(δ) = 0 that is not near the observed time series.”
Parallelised Bayesian Optimisation via Thompson Sampling (2018, methodology): “See [4, 20, 40] for more methods for selecting xj .”
Parameter estimation in biochemical pathways: a comparison of global optimization methods. (2003, methodology): “It is a version of the DIRECT algorithm (Jones et al. 1993; Jones 2001) that handles nonlinear and integer constraints.”
Bayesian Optimization in a Billion Dimensions via Random Embeddings (2013, methodology): “The optimization of the closed-form acquisition function can be carried out by oﬀ-the-shelf numerical optimization procedures, such as DIRECT (Jones et al., 1993) and CMA-ES (Hansen & Oster-meier, 2001).”