A Robust Gradient Sampling Algorithm for Nonsmooth, Nonconvex Optimization

By James V. Burke, A. S. Lewis, Michael L. Overton. 2005

542 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Numerical Analysis, Optimization & Training

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

In Computational Theory and Mathematics

In Numerical Analysis

In Optimization & Training

Citations in the corpus

A Convergence Theory for Deep Learning via Over-Parameterization (2018, background): “Even the general convergence for finding approximate critical points of a non-convex, non-smooth function is not fully understood (Burke et al., 2005), and appears to be a challenging question on its own.”
A Globally Convergent Algorithm for Nonconvex Optimization Based on Block Coordinate Update (2014, background): “Methods such as those in [6, 14, 16, 18] and the references therein and also books [8, 38] do not break variables into blocks.”
Nonsmooth H∞ synthesis (2005, background): “The authors have therefore developed a probabi listic algorithm which allows to treat problems like (7); see [3 1], [32].”
Nonsmooth optimization via quasi-Newton methods (2012, methodology): “This problem was one of the examples in [7]; in the results reported there, the objective function was defined without the logarithm and we enforced the semidefinite constraint by an exact penalty function.”
Control design for time-delay systems based on quasi-direct pole placement (2010, methodology): “As the spectral abscissa is a nonsmooth function, the gradient sampling algorithm was used, see [3,4].”
Classification and Review of Control Strategies for Plug-In Hybrid Electric Vehicles (2011, methodology): “There are many different methods that have been developed to solve this problem, including algorithms based on soothing techniques [22] and the random gradient sampling [23].”
Smoothing methods for nonsmooth, nonconvex minimization (2012, methodology): “Assume that f : Rn → R is locally Lipschitz, levelbounded, and continuously differentiable on an open dense subset of Rn [10,69].”
Smoothing and worst-case complexity for direct-search methods in nonsmooth optimization (2013, methodology): “Such smoothing functions were used in [24] to introduce a derivative-free version of the gradient sampling algorithm [5].”
An SQP Method Combined With Gradient Sampling for Small-Signal Stability Constrained OPF (2016, methodology): “In 2005 an algorithm known as Gradient Sampling (GS) was developed for nonsmooth unconstrained optimization problems [20].”
A Nonsmooth, Nonconvex Optimization Approach to Robust Stabilization by Static Output Feedback and Low-Order Controllers (2003, methodology): “However, we have devised a method based on gradient sampling that is very effective in practice and for which we have developed a local convergence theory (Burke et al., 2002; Burke et al., 2003b ).”