Global Optimization with Sparse and Local Gaussian Process Models

2015 ◽  
pp. 185-196 ◽  
Author(s):  
Tipaluck Krityakierne ◽  
David Ginsbourger
Keyword(s):  
Global Optimization ◽  
Gaussian Process ◽  
Process Models ◽  
Gaussian Process Models

scholarly journals Deterministic global optimization with Gaussian processes embedded

2021 ◽  
Author(s):  
Artur M. Schweidtmann ◽  
Dominik Bongartz ◽  
Daniel Grothe ◽  
Tim Kerkenhoff ◽  
Xiaopeng Lin ◽  
...  
Keyword(s):  
Global Optimization ◽  
Gaussian Process ◽  
Gaussian Processes ◽  
Optimization Problems ◽  
Process Models ◽  
Bayesian Optimization ◽  
Computational Time ◽  
Chance Constrained Programming ◽  
Deterministic Global Optimization ◽  
Gaussian Process Models

AbstractGaussian processes (Kriging) are interpolating data-driven models that are frequently applied in various disciplines. Often, Gaussian processes are trained on datasets and are subsequently embedded as surrogate models in optimization problems. These optimization problems are nonconvex and global optimization is desired. However, previous literature observed computational burdens limiting deterministic global optimization to Gaussian processes trained on few data points. We propose a reduced-space formulation for deterministic global optimization with trained Gaussian processes embedded. For optimization, the branch-and-bound solver branches only on the free variables and McCormick relaxations are propagated through explicit Gaussian process models. The approach also leads to significantly smaller and computationally cheaper subproblems for lower and upper bounding. To further accelerate convergence, we derive envelopes of common covariance functions for GPs and tight relaxations of acquisition functions used in Bayesian optimization including expected improvement, probability of improvement, and lower confidence bound. In total, we reduce computational time by orders of magnitude compared to state-of-the-art methods, thus overcoming previous computational burdens. We demonstrate the performance and scaling of the proposed method and apply it to Bayesian optimization with global optimization of the acquisition function and chance-constrained programming. The Gaussian process models, acquisition functions, and training scripts are available open-source within the “MeLOn—MachineLearning Models for Optimization” toolbox (https://git.rwth-aachen.de/avt.svt/public/MeLOn).

Identification of Continuous-time Nonlinear Systems via Local Gaussian Process Models

2014 ◽  
Vol 134 (11) ◽  
pp. 1708-1715
Author(s):  
Tomohiro Hachino ◽  
Kazuhiro Matsushita ◽  
Hitoshi Takata ◽  
Seiji Fukushima ◽  
Yasutaka Igarashi
Keyword(s):  
Nonlinear Systems ◽  
Gaussian Process ◽  
Continuous Time ◽  
Process Models ◽  
Gaussian Process Models

scholarly journals Composite Gaussian process models for emulating expensive functions

2012 ◽  
Vol 6 (4) ◽  
pp. 1838-1860 ◽  
Author(s):  
Shan Ba ◽  
V. Roshan Joseph
Keyword(s):  
Gaussian Process ◽  
Process Models ◽  
Gaussian Process Models
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