On the convergence of derivative-free methods for unconstrained optimization

By Andrew R. Conn, Katya Scheinberg, Philippe L. Toint. 1997

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Citations in the corpus

SentiNet: Detecting Localized Universal Attacks Against Deep Learning Systems (2018, methodology): “We then use our approximated curve to set classify attacks by calculating the distance between a curve and a point — using the Constrained Optimization by Linear Approximation (COBYLA) method [52]—and determining whether that distance is within a threshold estimated by the distances of clean example”
SentiNet: Detecting Physical Attacks Against Deep Learning Systems (2018, methodology): “and a point —using the Constrained Optimization by Linear Approximation (COBYLA) method [44]—and determining whether that distance is within a threshold estimated by the distances of clean examples lying outside the curve.”
Derivative-free optimization: a review of algorithms and comparison of software implementations (2012, background): “Recent works on the subject have led to significant progress by providing convergence proofs [5,9,31,34,76,80, 85,88,134], incorporating the use of surrogate models [22,24,127,131], and offering the first textbook that is exclusively devoted to this topic [35].”
UOBYQA: unconstrained optimization by quadratic approximation (2002, methodology): “Thus the updating tends to be beneficial to the interpolation equations (2), because, if the equations are written in matrix form by introducing any basis of the space of quadratic polynomials, then the replacement of xt by x̃t = xk +d multiplies the determinant of the matrix by the factor t(xk +d).”
Optimization by Direct Search: New Perspectives on Some Classical and Modern Methods (2003, methodology): “To further confuse matters, recently the term “derivative-free optimization” has been used with some frequency in the nonlinear programming literature to mean a number of methods that rely on derivative-free local models of the objective and constraints [71, 74, 177].”
Geometry of sample sets in derivative-free optimization: polynomial regression and underdetermined interpolation (2008, background): “These properties provide the foundation for using least-squares regression models in an algorithmic framework with global convergence properties (see [6, 7 , 10]).”
A rigorous framework for optimization of expensive functions by surrogates (1998, methodology): “Figure 1 presents run histories for two implementations of SMF, as well as the nal values obtained from nine runs of the DFO algorithm described in [8, 7].”
Polynomial interpolation in several variables (2000, methodology): “10) was used in [38] to prove the convergence of trust region algorithms for unconstraint derivative–free optimization.”
A new meta-heuristic algorithm for continuous engineering optimization: harmony search theory and practice (2005, unknown): “0) using gradient-based algorithms [32].”
Recent advances in trust region algorithms (2015, background): “Convergence results for derivative-free trust region algorithms are given in [26,30,103], and [136].”