A New Algorithm for Unconstrained Optimization

By M. Powell. 1970

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In Mathematical Optimization

Citations in the corpus

Survey of multifidelity methods in uncertainty propagation, inference, and optimization (2018, background): “Early formulations of trust-region ideas can be found in the papers by Levenberg [126] and Marquardt [136], with the papers by Powell [168, 169, 170] providing the important contribution of establishing and proving convergence of trust-region algorithms.”
Recent advances in trust region algorithms (2015, methodology): “…techniques to estimate the growing of the quasi-Newton matrices (see Powell [92]), while the global convergence of trust region type quasi-Newton methods can be easily established as long as the trace of the quasi-Newton matrices does not increase faster than linearly (see Powell [90]).”
ContactPose: A Dataset of Grasps with Object Contact and Hand Pose (2020, methodology): “It is optimized using the Dogleg [47] optimizer implemented in chumpy [2].”
Factor Graphs for Robot Perception (2017, background): “4 Dogleg Minimization Powell’s dogleg (PDL) algorithm [167] can be a more e cient alternative to LM [140].”
Recursive Trust-Region Methods for Multiscale Nonlinear Optimization (2008, methodology): “If, after completing one SCM cycle, one then notices that the overall step s lies outside of the trust region, we then apply a variant of the dogleg strategy (see [34], or [13], Section 7.”
Convergence of quasi-Newton matrices generated by the symmetric rank one update (1991, background): “(It is interesting to note that [12] has also been a seminal paper in the study of trust region methods.”
Historical development of the BFGS secant method and its characterization properties (2009, methodology): “While, Powell [96], in 1970, introduced the process of iterated projections and applied it to Broyden’s rank-one update, it was Dennis [33] who, in 1972, applied Powell’s method of iterated projections to the rank-one inverse update class (4.”
Quasi-Newton Methods: A New Direction (2012, background): “y = Bs V = I Broyden (1965) V = B Pearson (1969) McCormick V s = (y−Bs) SR1 (Davidon, 1959) y = Bs∧y = Bs V = I PSB (Powell, 1970) Greenstadt (1970) V = B DFP BFGS”
Full Waveform Inversion and the Truncated Newton Method (2013, methodology): “Different methods are proposed to solve this subproblem (see Moré [50] or the dogleg method [62]).”
Surrogate-Based Optimization Using Multifidelity Models with Variable Parameterization and Corrected Space Mapping (2008, methodology): “TRMM evolved from classical trust-region algorithms [14], which use quadratic surrogates, and has more recently been used for surrogates of any type [15].”