Optimization of black-box problems using Smolyak grids and polynomial approximations

[1]  Christodoulos A. Floudas,et al.  ARGONAUT: AlgoRithms for Global Optimization of coNstrAined grey-box compUTational problems , 2017, Optim. Lett..

[2]  Nikolaos V. Sahinidis,et al.  The ALAMO approach to machine learning , 2017, Comput. Chem. Eng..

[3]  Iftekhar A. Karimi,et al.  Smart Sampling Algorithm for Surrogate Model Development , 2017, Comput. Chem. Eng..

[4]  Lorenz T. Biegler,et al.  A trust region filter method for glass box/black box optimization , 2016 .

[5]  Christodoulos A. Floudas,et al.  Global optimization advances in Mixed-Integer Nonlinear Programming, MINLP, and Constrained Derivative-Free Optimization, CDFO , 2016, Eur. J. Oper. Res..

[6]  Bjarne Grimstad,et al.  Global optimization with spline constraints: a new branch-and-bound method based on B-splines , 2016, J. Glob. Optim..

[7]  Nikolaos V. Sahinidis,et al.  Simulation optimization: a review of algorithms and applications , 2014, 4OR.

[8]  Antonello Monti,et al.  Dimension-Adaptive Sparse Grid Interpolation for Uncertainty Quantification in Modern Power Systems: Probabilistic Power Flow , 2016, IEEE Transactions on Power Systems.

[9]  Dinh Dung,et al.  Sampling and Cubature on Sparse Grids Based on a B-spline Quasi-Interpolation , 2012, Found. Comput. Math..

[10]  Dirk Pflüger,et al.  Hierarchical Gradient-Based Optimization with B-Splines on Sparse Grids , 2016 .

[11]  Brendan Harding,et al.  Adaptive Sparse Grids and Extrapolation Techniques , 2016 .

[12]  C. Floudas,et al.  Global optimization of general constrained grey-box models: new method and its application to constrained PDEs for pressure swing adsorption , 2015, Journal of Global Optimization.

[13]  Alfio Quarteroni,et al.  A new algorithm for high-dimensional uncertainty quantification based on dimension-adaptive sparse grid approximation and reduced basis methods , 2015, J. Comput. Phys..

[14]  Guiqiao Xu,et al.  On weak tractability of the Smolyak algorithm for approximation problems , 2015, J. Approx. Theory.

[15]  Benjamin Peherstorfer,et al.  Selected Recent Applications of Sparse Grids , 2015 .

[16]  Isaac Siwale.  ON GLOBAL OPTIMIZATION , 2015 .

[17]  Selen Cremaschi,et al.  Adaptive sequential sampling for surrogate model generation with artificial neural networks , 2014, Comput. Chem. Eng..

[18]  Marianthi G. Ierapetritou,et al.  Derivative‐free optimization for expensive constrained problems using a novel expected improvement objective function , 2014 .

[19]  David C. Miller,et al.  Learning surrogate models for simulation‐based optimization , 2014 .

[20]  Edoardo Amaldi,et al.  PGS-COM: A hybrid method for constrained non-smooth black-box optimization problems: Brief review, novel algorithm and comparative evaluation , 2014, Comput. Chem. Eng..

[21]  R. Regis.  Constrained optimization by radial basis function interpolation for high-dimensional expensive black-box problems with infeasible initial points , 2014 .

[22]  Dirk Reith,et al.  SpaGrOW - A Derivative-Free Optimization Scheme for Intermolecular Force Field Parameters Based on Sparse Grid Methods , 2013, Entropy.

[23]  Lilia Maliar,et al.  Smolyak Method for Solving Dynamic Economic Models: Lagrange Interpolation, Anisotropic Grid and Adaptive Domain , 2013 .

[24]  Christine A. Shoemaker,et al.  A quasi-multistart framework for global optimization of expensive functions using response surface models , 2013, J. Glob. Optim..

[25]  Nikolaos V. Sahinidis,et al.  Derivative-free optimization: a review of algorithms and comparison of software implementations , 2013, J. Glob. Optim..

[26]  M. Ierapetritou,et al.  Surrogate-Based Optimization of Expensive Flowsheet Modeling for Continuous Pharmaceutical Manufacturing , 2013, Journal of Pharmaceutical Innovation.

[27]  Loo Hay Lee,et al.  Simulation optimization via kriging: a sequential search using expected improvement with computing budget constraints , 2013 .

[28]  Sébastien Le Digabel,et al.  Use of quadratic models with mesh-adaptive direct search for constrained black box optimization , 2011, Optim. Methods Softw..

[29]  Nélida E. Echebest,et al.  A derivative-free method for solving box-constrained underdetermined nonlinear systems of equations , 2012, Appl. Math. Comput..

[30]  Selen Cremaschi,et al.  Process synthesis of biodiesel production plant using artificial neural networks as the surrogate models , 2012, Comput. Chem. Eng..

[31]  Luc Pronzato,et al.  Design of computer experiments: space filling and beyond , 2011, Statistics and Computing.

[32]  Ying Jiang,et al.  B-spline quasi-interpolation on sparse grids , 2011, J. Complex..

[33]  L. Trefethen.  Six myths of polynomial interpolation and quadrature , 2011 .

[34]  W. Sickel,et al.  Spline interpolation on sparse grids , 2011 .

[35]  Tapan Mukerji,et al.  Derivative-Free Optimization for Oil Field Operations , 2011, Computational Optimization and Applications in Engineering and Industry.

[36]  M. Patriksson,et al.  A method for simulation based optimization using radial basis functions , 2010 .

[37]  Benjamin Peherstorfer,et al.  Spatially adaptive sparse grids for high-dimensional data-driven problems , 2010, J. Complex..

[38]  Xiaojun Chen,et al.  Error bounds for approximation in Chebyshev points , 2010, Numerische Mathematik.

[39]  Julio R. Banga,et al.  An evolutionary method for complex-process optimization , 2010, Comput. Oper. Res..

[40]  Christos T. Maravelias,et al.  Surrogate-Based Process Synthesis , 2010 .

[41]  A. I. F. Vaz,et al.  Optimizing radial basis functions by d.c. programming and its use in direct search for global derivative-free optimization , 2012 .

[42]  Marianthi G. Ierapetritou,et al.  A centroid-based sampling strategy for kriging global modeling and optimization , 2009 .

[43]  Sethuraman Sankaran,et al.  Stochastic optimization using a sparse grid collocation scheme , 2009 .

[44]  Marianthi G. Ierapetritou,et al.  A kriging based method for the solution of mixed-integer nonlinear programs containing black-box functions , 2009, J. Glob. Optim..

[45]  Charles Audet,et al.  A MADS Algorithm with a Progressive Barrier for Derivative-Free Nonlinear Programming , 2007 .

[46]  M. Powell.  The BOBYQA algorithm for bound constrained optimization without derivatives , 2009 .

[47]  I. Grossmann,et al.  An algorithm for the use of surrogate models in modular flowsheet optimization , 2008 .

[48]  Marianthi G. Ierapetritou,et al.  A Kriging-Based Approach to MINLP Containing Black-Box Models and Noise , 2008 .

[49]  Bengt Fornberg,et al.  The Runge phenomenon and spatially variable shape parameters in RBF interpolation , 2007, Comput. Math. Appl..

[50]  Julio R. Banga,et al.  Scatter search for chemical and bio-process optimization , 2007, J. Glob. Optim..

[51]  Dirk Pflüger,et al.  Adaptive Sparse Grid Techniques for Data Mining , 2006, HPSC.

[52]  Piotr Gajda,et al.  Smolyak's algorithm for weighted L1-approximation of multivariate functions with bounded rth mixed derivatives over ℝd , 2005, Numerical Algorithms.

[53]  Grzegorz W. Wasilkowski,et al.  Smolyak's Algorithm for Integration and L1-Approximation of Multivariate Functions with Bounded Mixed Derivatives of Second Order , 2004, Numerical Algorithms.

[54]  Hans-Joachim Bungartz,et al.  Higher Order Quadrature on Sparse Grids , 2004, International Conference on Computational Science.

[55]  H. Bungartz,et al.  Sparse grids , 2004, Acta Numerica.

[56]  Thomas Gerstner,et al.  Numerical integration using sparse grids , 2004, Numerical Algorithms.

[57]  Hans-Joachim Bungartz,et al.  Multivariate Quadrature on Adaptive Sparse Grids , 2003, Computing.

[58]  A. Keane,et al.  Evolutionary Optimization of Computationally Expensive Problems via Surrogate Modeling , 2003 .

[59]  Tamara G. Kolda,et al.  Optimization by Direct Search: New Perspectives on Some Classical and Modern Methods , 2003, SIAM Rev..

[60]  Matthew J. Realff,et al.  Optimization and Validation of Steady-State Flowsheet Simulation Metamodels , 2002 .

[61]  Donald R. Jones,et al.  A Taxonomy of Global Optimization Methods Based on Response Surfaces , 2001, J. Glob. Optim..

[62]  Hans-Martin Gutmann,et al.  A Radial Basis Function Method for Global Optimization , 2001, J. Glob. Optim..

[63]  Richard J. Beckman,et al.  A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output From a Computer Code , 2000, Technometrics.

[64]  Jean-François Richard,et al.  Methods of Numerical Integration , 2000 .

[65]  Erich Novak,et al.  High dimensional polynomial interpolation on sparse grids , 2000, Adv. Comput. Math..

[66]  Donald R. Jones,et al.  Efficient Global Optimization of Expensive Black-Box Functions , 1998, J. Glob. Optim..

[67]  A. J. Booker,et al.  A rigorous framework for optimization of expensive functions by surrogates , 1998 .

[68]  Erich Novak,et al.  Global Optimization Using Hyperbolic Cross Points , 1996 .

[69]  Henryk Wozniakowski,et al.  Explicit Cost Bounds of Algorithms for Multivariate Tensor Product Problems , 1995, J. Complex..

[70]  M. Powell.  A Direct Search Optimization Method That Models the Objective and Constraint Functions by Linear Interpolation , 1994 .

[71]  Wolfgang Hackbusch,et al.  Parallel algorithms for partial differential equations - Proceedings of the sixth GAMM-seminar - Kiel, January 19-21, 1990 , 1991 .

[72]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[73]  Robert Hooke,et al.  `` Direct Search'' Solution of Numerical and Statistical Problems , 1961, JACM.