Convergence of the Momentum Method for Semialgebraic Functions with Locally Lipschitz Gradients

Certifying the Absence of Spurious Local Minima at Infinity

(2023) Cédric Josz et al.   SIAM JOURNAL ON OPTIMIZATION

First-order methods almost always avoid strict saddle points

(2019) Jason D. Lee et al.   MATHEMATICAL PROGRAMMING

An inexact proximal gradient algorithm with extrapolation for a class of nonconvex nonsmooth optimization problems

(2019) Zehui Jia et al.   JOURNAL OF INEQUALITIES AND APPLICATIONS

Local Convergence of the Heavy-Ball Method and iPiano for Non-convex Optimization

(2018) Peter Ochs   JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS

Behavior of accelerated gradient methods near critical points of nonconvex functions

(2018) Michael O’Neill et al.   MATHEMATICAL PROGRAMMING

Calculus of the Exponent of Kurdyka–Łojasiewicz Inequality and Its Applications to Linear Convergence of First-Order Methods

(2017) Guoyin Li et al.   FOUNDATIONS OF COMPUTATIONAL MATHEMATICS

Linear Convergence of Proximal Gradient Algorithm with Extrapolation for a Class of Nonconvex Nonsmooth Minimization Problems

(2017) Bo Wen et al.   SIAM JOURNAL ON OPTIMIZATION

Accelerated gradient methods for nonconvex nonlinear and stochastic programming

(2015) Saeed Ghadimi et al.   MATHEMATICAL PROGRAMMING

iPiano: Inertial Proximal Algorithm for Nonconvex Optimization

(2014) Peter Ochs et al.   SIAM Journal on Imaging Sciences

Proximal alternating linearized minimization for nonconvex and nonsmooth problems

(2013) Jérôme Bolte et al.   MATHEMATICAL PROGRAMMING

Convergence of descent methods for semi-algebraic and tame problems: proximal algorithms, forward–backward splitting, and regularized Gauss–Seidel methods

(2011) Hedy Attouch et al.   MATHEMATICAL PROGRAMMING