Derivative-free optimization methods

Larson, Jeffrey; Menickelly, Matt; Wild, Stefan M.

doi:10.1017/S0962492919000060

Title: Derivative-free optimization methods

Journal Article · 01 May 2019 · Acta Numerica

DOI: https://doi.org/10.1017/S0962492919000060 · OSTI ID:1545343

Larson, Jeffrey ^[1]; Menickelly, Matt ^[1]; Wild, Stefan M. ^[1]

Argonne National Lab. (ANL), Argonne, IL (United States)

In many optimization problems arising from scientific, engineering and artificial intelligence applications, objective and constraint functions are available only as the output of a black-box or simulation oracle that does not provide derivative information. Such settings necessitate the use of methods for derivative-free, or zeroth-order, optimization. We provide a review and perspectives on developments in these methods, with an emphasis on highlighting recent developments and on unifying treatment of such problems in the non-linear optimization and machine learning literature. We categorize methods based on assumed properties of the black-box functions, as well as features of the methods. We first overview the primary setting of deterministic methods applied to unconstrained, non-convex optimization problems where the objective function is defined by a deterministic black-box oracle. We then discuss developments in randomized methods, methods that assume some additional structure about the objective (including convexity, separability and general non-smooth compositions), methods for problems where the output of the black-box oracle is stochastic, and methods for handling different types of constraints.

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Research Organization:: Argonne National Laboratory (ANL)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)

Grant/Contract Number:: AC02-06CH11357

OSTI ID:: 1545343

Journal Information:: Acta Numerica, Journal Name: Acta Numerica Journal Issue: 2010 Vol. 28; ISSN 0962-4929

Publisher:: Cambridge University PressCopyright Statement

Country of Publication:: United States

Language:: English

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A Globally Convergent Filter Method for Nonlinear Programming Gonzaga, Clóvis C.; Karas, Elizabeth; Vanti, Márcia SIAM Journal on Optimization, Vol. 14, Issue 3 https://doi.org/10.1137/S1052623401399320	journal	January 2004
Stationarity Results for Generating Set Search for Linearly Constrained Optimization Kolda, Tamara G.; Lewis, Robert Michael; Torczon, Virginia SIAM Journal on Optimization, Vol. 17, Issue 4 https://doi.org/10.1137/S1052623403433638	journal	January 2007
On the Convergence of Pattern Search Algorithms Torczon, Virginia SIAM Journal on Optimization, Vol. 7, Issue 1 https://doi.org/10.1137/S1052623493250780	journal	February 1997
Budget-Dependent Convergence Rate of Stochastic Approximation L'Ecuyer, Pierre; Yin, George SIAM Journal on Optimization, Vol. 8, Issue 1 https://doi.org/10.1137/S1052623495270723	journal	February 1998
Fortified-Descent Simplicial Search Method: A General Approach Tseng, Paul SIAM Journal on Optimization, Vol. 10, Issue 1 https://doi.org/10.1137/S1052623495282857	journal	January 1999
Pattern Search Algorithms for Bound Constrained Minimization Lewis, Robert Michael; Torczon, Virginia SIAM Journal on Optimization, Vol. 9, Issue 4 https://doi.org/10.1137/S1052623496300507	journal	January 1999
Convergence Properties of the Nelder--Mead Simplex Method in Low Dimensions Lagarias, Jeffrey C.; Reeds, James A.; Wright, Margaret H. SIAM Journal on Optimization, Vol. 9, Issue 1 https://doi.org/10.1137/S1052623496303470	journal	January 1998
Convergence of the Nelder--Mead Simplex Method to a Nonstationary Point McKinnon, K. I. M. SIAM Journal on Optimization, Vol. 9, Issue 1 https://doi.org/10.1137/S1052623496303482	journal	January 1998
Detection and Remediation of Stagnation in the Nelder--Mead Algorithm Using a Sufficient Decrease Condition Kelley, C. T. SIAM Journal on Optimization, Vol. 10, Issue 1 https://doi.org/10.1137/S1052623497315203	journal	January 1999
On the Global Convergence of Derivative-Free Methods for Unconstrained Optimization Lucidi, Stefano; Sciandrone, Marco SIAM Journal on Optimization, Vol. 13, Issue 1 https://doi.org/10.1137/S1052623497330392	journal	January 2002
Pattern Search Methods for Linearly Constrained Minimization Lewis, Robert Michael; Torczon, Virginia SIAM Journal on Optimization, Vol. 10, Issue 3 https://doi.org/10.1137/S1052623497331373	journal	January 2000
A Globally Convergent Augmented Lagrangian Pattern Search Algorithm for Optimization with General Constraints and Simple Bounds Lewis, Robert Michael; Torczon, Virginia SIAM Journal on Optimization, Vol. 12, Issue 4 https://doi.org/10.1137/S1052623498339727	journal	January 2002
A Class of Trust-Region Methods for Parallel Optimization Hough, P. D.; Meza, J. C. SIAM Journal on Optimization, Vol. 13, Issue 1 https://doi.org/10.1137/S1052623498343799	journal	January 2002
Pattern Search Algorithms for Mixed Variable Programming Audet, Charles; Dennis, J. E. SIAM Journal on Optimization, Vol. 11, Issue 3 https://doi.org/10.1137/S1052623499352024	journal	January 2001
Superlinear Convergence and Implicit Filtering Choi, T. D.; Kelley, C. T. SIAM Journal on Optimization, Vol. 10, Issue 4 https://doi.org/10.1137/S1052623499354096	journal	January 2000
Asynchronous Parallel Pattern Search for Nonlinear Optimization Hough, Patricia D.; Kolda, Tamara G.; Torczon, Virginia J. SIAM Journal on Scientific Computing, Vol. 23, Issue 1 https://doi.org/10.1137/S1064827599365823	journal	January 2001
Algorithm 856: APPSPACK 4.0: asynchronous parallel pattern search for derivative-free optimization Gray, Genetha A.; Kolda, Tamara G. ACM Transactions on Mathematical Software, Vol. 32, Issue 3 https://doi.org/10.1145/1163641.1163647	journal	September 2006
SNOBFIT -- Stable Noisy Optimization by Branch and Fit Huyer, Waltraud; Neumaier, Arnold ACM Transactions on Mathematical Software, Vol. 35, Issue 2 https://doi.org/10.1145/1377612.1377613	journal	July 2008
Algorithm 897: VTDIRECT95: Serial and parallel codes for the global optimization algorithm direct He, Jian; Watson, Layne T.; Sosonkina, Masha ACM Transactions on Mathematical Software, Vol. 36, Issue 3 https://doi.org/10.1145/1527286.1527291	journal	July 2009
Algorithm 909: NOMAD: Nonlinear Optimization with the MADS Algorithm Le Digabel, Sébastien ACM Transactions on Mathematical Software, Vol. 37, Issue 4 https://doi.org/10.1145/1916461.1916468	journal	February 2011
Estimating Derivatives of Noisy Simulations Moré, Jorge J.; Wild, Stefan M. ACM Transactions on Mathematical Software, Vol. 38, Issue 3 https://doi.org/10.1145/2168773.2168777	journal	April 2012
Kernel-based methods for Bandit convex optimization Bubeck, Sébastien; Lee, Yin Tat; Eldan, Ronen Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing - STOC 2017 https://doi.org/10.1145/3055399.3055403	conference	January 2017
BFO, A Trainable Derivative-free Brute Force Optimizer for Nonlinear Bound-constrained Optimization and Equilibrium Computations with Continuous and Discrete Variables Porcelli, Margherita; Toint, Philippe L. ACM Transactions on Mathematical Software, Vol. 44, Issue 1 https://doi.org/10.1145/3085592	journal	June 2017
Google Vizier: A Service for Black-Box Optimization Golovin, Daniel; Solnik, Benjamin; Moitra, Subhodeep KDD '17: The 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Proceedings of the 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining https://doi.org/10.1145/3097983.3098043	conference	August 2017
`` Direct Search'' Solution of Numerical and Statistical Problems Hooke, Robert; Jeeves, T. A. Journal of the ACM, Vol. 8, Issue 2 https://doi.org/10.1145/321062.321069	journal	April 1961
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A View of Unconstrained Minimization Algorithms that Do Not Require Derivatives Powell, M. J. D. ACM Transactions on Mathematical Software, Vol. 1, Issue 2 https://doi.org/10.1145/355637.355638	journal	June 1975
An effective algorithm for hyperparameter optimization of neural networks Diaz, G. I.; Fokoue-Nkoutche, A.; Nannicini, G. IBM Journal of Research and Development, Vol. 61, Issue 4/5 https://doi.org/10.1147/JRD.2017.2709578	journal	July 2017
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