Stochastic derivative-free optimization of noisy functions

1

[1]  Nello Cristianini,et al.  An Introduction to Support Vector Machines and Other Kernel-based Learning Methods , 2000 .

[2]  Stefan M. Wild,et al.  Non-intrusive termination of noisy optimization , 2013, Optim. Methods Softw..

[3]  N P Willassen,et al.  Purification and characterization of pancreatic elastase from North Atlantic salmon (Salmo salar). , 1998, Molecular marine biology and biotechnology.

[4]  Lydia E. Kavraki,et al.  The MASH Pipeline for Protein Function Prediction and an Algorithm for the Geometric Refinement of 3D Motifs , 2007, J. Comput. Biol..

[5]  Virginia Torczon,et al.  On the Convergence of the Multidirectional Search Algorithm , 1991, SIAM J. Optim..

[6]  V. Torczon,et al.  Direct search methods: then and now , 2000 .

[7]  J. Kiefer,et al.  Stochastic Estimation of the Maximum of a Regression Function , 1952 .

[8]  G L Kenyon,et al.  Mechanism of the reaction catalyzed by mandelate racemase: structure and mechanistic properties of the D270N mutant. , 1995, Biochemistry.

[9]  K Morihara,et al.  Comparison of the specificities of various serine proteinases from microorganisms. , 1969, Archives of biochemistry and biophysics.

[10]  Jeffrey Larson,et al.  DERIVATIVE-FREE OPTIMIZATION OF NOISY FUNCTIONS , 2012 .

[11]  C. D. Perttunen,et al.  Lipschitzian optimization without the Lipschitz constant , 1993 .

[12]  Michael C. Ferris,et al.  Classification-Based Global Search: an Application to a Simulation for Breast Cancer , 2008 .

[13]  G. H. Reed,et al.  The enolase superfamily: a general strategy for enzyme-catalyzed abstraction of the alpha-protons of carboxylic acids. , 1996, Biochemistry.

[14]  C. T. Kelley,et al.  An Implicit Filtering Algorithm for Optimization of Functions with Many Local Minima , 1995, SIAM J. Optim..

[15]  C Sander,et al.  Mapping the Protein Universe , 1996, Science.

[16]  Lei Xie,et al.  Detecting evolutionary relationships across existing fold space, using sequence order-independent profile–profile alignments , 2008, Proceedings of the National Academy of Sciences.

[17]  Russell R. Barton,et al.  Sample size selection for improved Nelder-Mead performance , 1995, WSC '95.

[18]  Katya Scheinberg,et al.  Recent progress in unconstrained nonlinear optimization without derivatives , 1997, Math. Program..

[19]  Saeed Ghadimi,et al.  Stochastic First- and Zeroth-Order Methods for Nonconvex Stochastic Programming , 2013, SIAM J. Optim..

[20]  R. Durrett.  Probability: Theory and Examples , 1993 .

[21]  Martin Berz,et al.  Computational differentiation : techniques, applications, and tools , 1996 .

[22]  John L. Nazareth,et al.  Introduction to derivative-free optimization , 2010, Math. Comput..

[23]  Vincent B. Chen,et al.  Correspondence e-mail: , 2000 .

[24]  M. J. D. Powell,et al.  UOBYQA: unconstrained optimization by quadratic approximation , 2002, Math. Program..

[25]  O. SIAMJ.,et al.  ON THE CONVERGENCE OF PATTERN SEARCH ALGORITHMS , 1997 .

[26]  Stefan M. Wild,et al.  Estimating Derivatives of Noisy Simulations , 2012, TOMS.

[27]  Jie Liang,et al.  pvSOAR: detecting similar surface patterns of pocket and void surfaces of amino acid residues on proteins , 2004, Nucleic Acids Res..

[28]  Jens Jägersküpper,et al.  How the (1+1) ES using isotropic mutations minimizes positive definite quadratic forms , 2006, Theor. Comput. Sci..

[29]  Nicholas I. M. Gould,et al.  Trust Region Methods , 2000, MOS-SIAM Series on Optimization.

[30]  Mikhail Bilenko,et al.  Lazy Paired Hyper-Parameter Tuning , 2013, IJCAI.

[31]  Brian Yuan Chen,et al.  A statistical model of overlapping volume in ligand binding cavities , 2011, 2011 IEEE International Conference on Bioinformatics and Biomedicine Workshops (BIBMW).

[32]  Jeffrey Larson,et al.  Stochastic derivative-free optimization using a trust region framework , 2016, Comput. Optim. Appl..

[33]  Michael C. Ferris,et al.  A Direct Search Algorithm for Optimization with Noisy Function Evaluations , 2000, SIAM J. Optim..

[34]  Anne Auger,et al.  Convergence results for the (1, lambda)-SA-ES using the theory of phi-irreducible Markov chains , 2005, Theor. Comput. Sci..

[35]  Stefan M. Wild,et al.  Benchmarking Derivative-Free Optimization Algorithms , 2009, SIAM J. Optim..

[36]  B Honig,et al.  An integrated approach to the analysis and modeling of protein sequences and structures. I. Protein structural alignment and a quantitative measure for protein structural distance. , 2000, Journal of molecular biology.

[37]  Stefan M. Wild,et al.  Do you trust derivatives or differences? , 2014, Journal of Computational Physics.

[38]  Charles Audet,et al.  Mesh Adaptive Direct Search Algorithms for Constrained Optimization , 2006, SIAM J. Optim..

[39]  Lydia E. Kavraki,et al.  Geometric Sieving: Automated Distributed Optimization of 3D Motifs for Protein Function Prediction , 2006, RECOMB.

[40]  Hans-Paul Schwefel,et al.  Evolution strategies – A comprehensive introduction , 2002, Natural Computing.

[41]  L. N. Vicente,et al.  Geometry of sample sets in derivative-free optimization: polynomial regression and underdetermined interpolation , 2008 .

[42]  William E. Lorensen,et al.  Marching cubes: A high resolution 3D surface construction algorithm , 1987, SIGGRAPH.

[43]  Jeffrey Larson,et al.  Derivative-Free Optimization of Expensive Functions with Computational Error Using Weighted Regression , 2013, SIAM J. Optim..

[44]  Yurii Nesterov,et al.  Random Gradient-Free Minimization of Convex Functions , 2015, Foundations of Computational Mathematics.

[45]  Arnold Neumaier,et al.  SNOBFIT -- Stable Noisy Optimization by Branch and Fit , 2008, TOMS.

[46]  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.

[47]  Anne Auger,et al.  Log-Linear Convergence and Divergence of the Scale-Invariant (1+1)-ES in Noisy Environments , 2011, Algorithmica.

[48]  Charles Audet,et al.  OrthoMADS: A Deterministic MADS Instance with Orthogonal Directions , 2008, SIAM J. Optim..

[49]  O. Nelles,et al.  An Introduction to Optimization , 1996, IEEE Antennas and Propagation Magazine.

[50]  K. Sharp,et al.  Accurate Calculation of Hydration Free Energies Using Macroscopic Solvent Models , 1994 .

[51]  M. G. Stone,et al.  Face Traverses and a Volume Algorithm for Polyhedra , 1991, New Results and New Trends in Computer Science.

[52]  Michael C. Ferris,et al.  Adaptation of the Uobyqa Algorithm for Noisy Functions , 2006, Proceedings of the 2006 Winter Simulation Conference.

[53]  M. J. D. Powell,et al.  On trust region methods for unconstrained minimization without derivatives , 2003, Math. Program..

[54]  James C. Spall,et al.  Adaptive stochastic approximation by the simultaneous perturbation method , 2000, IEEE Trans. Autom. Control..

[55]  Brian Yuan Chen,et al.  VASP-S: A Volumetric Analysis and Statistical Model for Predicting Steric Influences on Protein-Ligand Binding Specificity , 2011, 2011 IEEE International Conference on Bioinformatics and Biomedicine.

[56]  R. Tibshirani.  Regression Shrinkage and Selection via the Lasso , 1996 .

[57]  Ambuj Tewari,et al.  Smoothness, Low Noise and Fast Rates , 2010, NIPS.

[58]  B. Luisi,et al.  Crystal structure of the Escherichia coli RNA degradosome component enolase. , 2001, Journal of molecular biology.

[59]  Katya Scheinberg,et al.  Convergence of Trust-Region Methods Based on Probabilistic Models , 2013, SIAM J. Optim..

[60]  L Szilágyi,et al.  Electrostatic complementarity within the substrate-binding pocket of trypsin. , 1988, Proceedings of the National Academy of Sciences of the United States of America.

[61]  Katya Scheinberg,et al.  Global Convergence of General Derivative-Free Trust-Region Algorithms to First- and Second-Order Critical Points , 2009, SIAM J. Optim..

[62]  Adam Godzik,et al.  Multiple flexible structure alignment using partial order graphs , 2005, Bioinform..

[63]  Michael C. Ferris,et al.  Extension of the direct optimization algorithm for noisy functions , 2007, 2007 Winter Simulation Conference.

[64]  C. T. Kelley,et al.  Detection and Remediation of Stagnation in the Nelder--Mead Algorithm Using a Sufficient Decrease Condition , 1999, SIAM J. Optim..

[65]  Stefan M. Wild,et al.  Estimating Computational Noise , 2011, SIAM J. Sci. Comput..

[66]  Katya Scheinberg,et al.  Geometry of interpolation sets in derivative free optimization , 2007, Math. Program..

[67]  Christian L. Müller,et al.  Optimization of Convex Functions with Random Pursuit , 2011, SIAM J. Optim..

[68]  K. Kinoshita,et al.  Identification of the ligand binding sites on the molecular surface of proteins , 2005, Protein science : a publication of the Protein Society.

[69]  B. Honig,et al.  An integrated approach to the analysis and modeling of protein sequences and structures. III. A comparative study of sequence conservation in protein structural families using multiple structural alignments. , 2000, Journal of molecular biology.

[70]  M. Powell.  The NEWUOA software for unconstrained optimization without derivatives , 2006 .

[71]  Charles Audet,et al.  Convergence of Mesh Adaptive Direct Search to Second-Order Stationary Points , 2006, SIAM J. Optim..

[72]  Sham M. Kakade,et al.  Stochastic Convex Optimization with Bandit Feedback , 2011, SIAM J. Optim..

[73]  Barry Honig,et al.  VASP: A Volumetric Analysis of Surface Properties Yields Insights into Protein-Ligand Binding Specificity , 2010, PLoS Comput. Biol..

[74]  Katya Scheinberg,et al.  On the convergence of derivative-free methods for unconstrained optimization , 1997 .

[75]  M. Powell.  Developments of NEWUOA for minimization without derivatives , 2008 .

[76]  Katya Scheinberg,et al.  Aligning ligand binding cavities by optimizing superposed volume , 2012, 2012 IEEE International Conference on Bioinformatics and Biomedicine.

[77]  Robert D. Nowak,et al.  Query Complexity of Derivative-Free Optimization , 2012, NIPS.

[78]  T. N. Bhat,et al.  The Protein Data Bank , 2000, Nucleic Acids Res..

[79]  K. Steiglitz,et al.  Adaptive step size random search , 1968 .

[80]  P E Bourne,et al.  Protein structure alignment by incremental combinatorial extension (CE) of the optimal path. , 1998, Protein engineering.

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

[82]  W R Taylor,et al.  SSAP: sequential structure alignment program for protein structure comparison. , 1996, Methods in enzymology.

[83]  Charles Audet,et al.  Nonsmooth optimization through Mesh Adaptive Direct Search and Variable Neighborhood Search , 2006, J. Glob. Optim..

[84]  Katya Scheinberg,et al.  A derivative free optimization algorithm in practice , 1998 .

[85]  A. Auger.  Convergence results for the ( 1 , )-SA-ES using the theory of-irreducible Markov chains , 2005 .