I will describe multiple (parallel) global optimization algorithms utilizing iteratively constructed surrogate approximations with continuous and/or integer variables that are available as open source software PySOT (18,000 downloads). The numerical results shown will indicate our surrogate algorithms are very effective on test problems and on complex real applications including machine learning and Carbon Sequestration. In particular, the Radial Basis methods significantly and consistently outperform (sometimes over three times faster for same accuracy) Gaussian Process + Expected Improvement algorithms for global optimization with dimensions 10 or above. SOARS is our surrogate-based MCMC method. Speedups of over 20 are obtained for SOARS compared to conventional MCMC. Optimization and UQ applications to objective functions that are nonlinear PDE simulations arising in environmental protection will be presented. Many co-authors have been involved in these papers and codes.
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