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Optimization Methods and Software Volume 24, 2009 - Issue 1
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Original Articles

On the geometry phase in model-based algorithms for derivative-free optimization

Giovanni Fasano Dipartimento di Matematica Applicata, Universita`'Foscari di Venezia and INSEAN, Venezia, Italy
,
José Luis Morales Departamento de Matemáticas, Instituto Tecnológico Autónomo de México, México, Mexico
&
Jorge Nocedal Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, USACorrespondence[email protected]
Pages 145-154 | Received 15 Mar 2008, Published online: 04 Mar 2011

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A. S. Berahas, O. Sohab & L. N. Vicente. (2023) Full-low evaluation methods for derivative-free optimization. Optimization Methods and Software 38:2, pages 386-411.
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James C. Gross & Geoffrey T. Parks. (2022) Optimization by moving ridge functions: derivative-free optimization for computationally intensive functions. Engineering Optimization 54:4, pages 553-575.
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P. S. Ferreira, E. W. Karas, M. Sachine & F. N. C. Sobral. (2017) Global convergence of a derivative-free inexact restoration filter algorithm for nonlinear programming. Optimization 66:2, pages 271-292.
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P.D. Conejo, E.W. Karas & L.G. Pedroso. (2015) A trust-region derivative-free algorithm for constrained optimization. Optimization Methods and Software 30:6, pages 1126-1145.
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S. Gratton & L. N. Vicente. (2014) A surrogate management framework using rigorous trust-region steps. Optimization Methods and Software 29:1, pages 10-23.
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Andrew R. Conn & Sébastien Le Digabel. (2013) Use of quadratic models with mesh-adaptive direct search for constrained black box optimization. Optimization Methods and Software 28:1, pages 139-158.
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A. R. Conn & L. N. Vicente. (2012) Bilevel derivative-free optimization and its application to robust optimization. Optimization Methods and Software 27:3, pages 561-577.
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Serge Gratton, Philippe L. Toint & Anke Tröltzsch. (2011) An active-set trust-region method for derivative-free nonlinear bound-constrained optimization. Optimization Methods and Software 26:4-5, pages 873-894.
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A. L. Custódio, R. Garmanjani & M. Raydan. (2023) Derivative-free separable quadratic modeling and cubic regularization for unconstrained optimization. 4OR.
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Lingyun He, Peng Wang & Detong Zhu. (2021) Projected Adaptive Cubic Regularization Algorithm with Derivative-Free Filter Technique for Box Constrained Optimization. Discrete Dynamics in Nature and Society 2021, pages 1-13.
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Ian D. Coope & Rachael Tappenden. (2021) Gradient and diagonal Hessian approximations using quadratic interpolation models and aligned regular bases. Numerical Algorithms 88:2, pages 767-791.
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Neculai AndreiNeculai Andrei. 2021. A Derivative-free Two Level Random Search Method for Unconstrained Optimization. A Derivative-free Two Level Random Search Method for Unconstrained Optimization 1 17 .
Andrea Manno, Edoardo Amaldi, Francesco Casella & Emanuele Martelli. (2020) A local search method for costly black-box problems and its application to CSP plant start-up optimization refinement. Optimization and Engineering 21:4, pages 1563-1598.
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Jeffrey Larson, Matt Menickelly & Stefan M. Wild. (2019) Derivative-free optimization methods. Acta Numerica 28, pages 287-404.
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Serge Gratton, Clément W Royer, Luís N Vicente & Zaikun Zhang. (2018) Complexity and global rates of trust-region methods based on probabilistic models. IMA Journal of Numerical Analysis 38:3, pages 1579-1597.
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Alvaro Maggiar, Andreas Wächter, Irina S. Dolinskaya & Jeremy Staum. (2018) A Derivative-Free Trust-Region Algorithm for the Optimization of Functions Smoothed via Gaussian Convolution Using Adaptive Multiple Importance Sampling. SIAM Journal on Optimization 28:2, pages 1478-1507.
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Jueyu Wang & Detong Zhu. (2016) Conjugate gradient path method without line search technique for derivative-free unconstrained optimization. Numerical Algorithms 73:4, pages 957-983.
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Anke Tr?ltzsch. (2014) A sequential quadratic programming algorithm for equality-constrained optimization without derivatives. Optimization Letters 10:2, pages 383-399.
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R. Garmanjani, D. J?dice & L. N. Vicente. (2016) Trust-Region Methods Without Using Derivatives: Worst Case Complexity and the NonSmooth Case. SIAM Journal on Optimization 26:4, pages 1987-2011.
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Ya-xiang Yuan. (2015) Recent advances in trust region algorithms. Mathematical Programming 151:1, pages 249-281.
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Ph. R. Sampaio & Ph. L. Toint. (2014) A derivative-free trust-funnel method for equality-constrained nonlinear optimization. Computational Optimization and Applications 61:1, pages 25-49.
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Sandra A. Santos. (2014) TRUST-REGION-BASED METHODS FOR NONLINEAR PROGRAMMING: RECENT ADVANCES AND PERSPECTIVES. Pesquisa Operacional 34:3, pages 447-462.
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Jon S. Dæhlen, Gisle Otto Eikrem & Tor Arne Johansen. (2014) Nonlinear model predictive control using trust-region derivative-free optimization. Journal of Process Control 24:7, pages 1106-1120.
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A. S. Bandeira, K. Scheinberg & L. N. Vicente. (2014) Convergence of Trust-Region Methods Based on Probabilistic Models. SIAM Journal on Optimization 24:3, pages 1238-1264.
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Valeri Sulimov & Pavel Shkapov. (2013) Hybrid algorithms for optimization of hydro-mechanical systems with derivative-free local search. Science and Education of the Bauman MSTU 13:12.
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P.D. Conejo, E.W. Karas, L.G. Pedroso, A.A. Ribeiro & M. Sachine. (2013) Global convergence of trust-region algorithms for convex constrained minimization without derivatives. Applied Mathematics and Computation 220, pages 324-330.
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Hui Zhao, Gaoming Li, Albert C. Reynolds & Jun Yao. (2012) Large-scale history matching with quadratic interpolation models. Computational Geosciences 17:1, pages 117-138.
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Stefan M. Wild & Christine Shoemaker. (2013) Global Convergence of Radial Basis Function Trust-Region Algorithms for Derivative-Free Optimization. SIAM Review 55:2, pages 349-371.
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A. S. Bandeira, K. Scheinberg & L. N. Vicente. (2012) Computation of sparse low degree interpolating polynomials and their application to derivative-free optimization. Mathematical Programming 134:1, pages 223-257.
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Coralia Cartis, Nicholas I. M. Gould & Philippe L. Toint. (2012) On the Oracle Complexity of First-Order and Derivative-Free Algorithms for Smooth Nonconvex Minimization. SIAM Journal on Optimization 22:1, pages 66-86.
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Stefan M. Wild & Christine Shoemaker. (2011) Global Convergence of Radial Basis Function Trust Region Derivative-Free Algorithms. SIAM Journal on Optimization 21:3, pages 761-781.
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Qing Hua Zhou, Feng Xia Xu, Yan Geng & Ya Rui Zhang. (2011) A Note on Wedge Trust Region Radius Update. Applied Mechanics and Materials 52-54, pages 926-931.
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A. L. Custódio, H. Rocha & L. N. Vicente. (2009) Incorporating minimum Frobenius norm models in direct search. Computational Optimization and Applications 46:2, pages 265-278.
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K. Scheinberg & Ph. L. Toint. (2010) Self-Correcting Geometry in Model-Based Algorithms for Derivative-Free Unconstrained Optimization. SIAM Journal on Optimization 20:6, pages 3512-3532.
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