Recursive Trust-Region Methods for Multiscale Nonlinear Optimization

By Serge Gratton, Annick Sartenaer, Philippe L. Toint. 2008

217 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Numerical Analysis

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Citations in the corpus

Accelerated gradient methods for nonconvex nonlinear and stochastic programming (2013, background): “at most O(1/ǫ) iterations, which is the best-known complexity bound possessed by ﬁrst-order methods to solve general NLP problems (e.g., the gradient descent method [25,4] and the trust region method [30]). Note that if Ψ is convex and a more aggressive stepsize policy is applied in the AG method, t”
Smoothing and worst-case complexity for direct-search methods in nonsmooth optimization (2013, methodology): “Gratton, Toint, and co-authors [20, 21] and Cartis, Gould, and Toint [6] proved a similar worst case complexity bound of O(ǫ−2) for trust-region methods and adaptive cubic overestimation methods, respectively, when these algorithms are based on a Cauchy decrease condition.”
On the Oracle Complexity of First-Order and Derivative-Free Algorithms for Smooth Nonconvex Minimization (2012, background): “…Nesterov 2004, 2008, Nemirovski, 1994, Agarwal, Bartlett, Ravikummar and Wainwright, 2009), but also for the nonconvex case (see Vavasis 1992b, 1992a, 1993, Nesterov and Polyak, 2006, Gratton, Sartenaer and Toint, 2008, Cartis, Gould and Toint 2011a, 2010a, 2010b, 2011b, or Vicente, 2010).”
Worst case complexity of direct search (2013, methodology): “A similar worst case complexity bound of O ( (cid:15) − 2 ) has been proved by Gratton, Toint, and co-authors [10, 11] for trust-region methods and by Cartis, Gould, and Toint [3] for adaptive cubic overestimation methods, when these algorithms are based on a Cauchy decrease condition.”
Adaptive cubic regularisation methods for unconstrained optimization. Part II: worst-case function- and derivative-evaluation complexity (2011, result): “Similar complexity results for trust-region methods are given in [6,7].”
Recent advances in trust region algorithms (2015, methodology): “A class of recursive trust region methods for multiscale nonlinear optimization, often arising in systems governed by partial differential equations, is given by by Gratton et al. [63].”
Complexity and global rates of trust-region methods based on probabilistic models (2018, methodology): “Using firstorder Taylor expansions as models, trust-region methods are known [20] to take at most O( −2) iterations1 to reduce the measure ‖∇f(·)‖ below ∈ (0, 1).”