Fast convex optimization via inertial dynamics with Hessian driven damping

[1]  R. A. Silverman,et al.  Special functions and their applications , 1966 .

[2]  Z. Opial Weak convergence of the sequence of successive approximations for nonexpansive mappings , 1967 .

[3]  R. A. Silverman,et al.  Special functions and their applications , 1966 .

[4]  Ronald E. Bruck Asymptotic convergence of nonlinear contraction semigroups in Hilbert space , 1975 .

[5]  H. Brezis Asymptotic Behavior of Some Evolution Systems , 1978 .

[6]  Y. Nesterov A method for solving the convex programming problem with convergence rate O(1/k^2) , 1983 .

[7]  Felipe Alvarez,et al.  On the Minimizing Property of a Second Order Dissipative System in Hilbert Spaces , 2000, SIAM J. Control. Optim..

[8]  H. Attouch,et al.  THE HEAVY BALL WITH FRICTION METHOD, I. THE CONTINUOUS DYNAMICAL SYSTEM: GLOBAL EXPLORATION OF THE LOCAL MINIMA OF A REAL-VALUED FUNCTION BY ASYMPTOTIC ANALYSIS OF A DISSIPATIVE DYNAMICAL SYSTEM , 2000 .

[9]  CONVERGENCE AND ASYMPTOTIC STABILIZATION FOR SOME DAMPED HYPERBOLIC EQUATIONS WITH NON-ISOLATED EQUILIBRIA , 2001 .

[10]  H. Attouch,et al.  An Inertial Proximal Method for Maximal Monotone Operators via Discretization of a Nonlinear Oscillator with Damping , 2001 .

[11]  H. Attouch,et al.  Asymptotic Control and Stabilization of Nonlinear Oscillators with Non-isolated Equilibria , 2002 .

[12]  J. Bolte,et al.  A second-order gradient-like dissipative dynamical system with Hessian-driven damping.: Application to optimization and mechanics , 2002 .

[13]  A. Moudafi,et al.  Convergence of a splitting inertial proximal method for monotone operators , 2003 .

[14]  Yurii Nesterov,et al.  Introductory Lectures on Convex Optimization - A Basic Course , 2014, Applied Optimization.

[15]  A. Cabot Inertial Gradient-Like Dynamical System Controlled by a Stabilizing Term , 2004 .

[16]  Yurii Nesterov,et al.  Smooth minimization of non-smooth functions , 2005, Math. Program..

[17]  Samir Adly,et al.  Finite Time Stabilization of Nonlinear Oscillators Subject to dry Friction , 2006 .

[18]  Y. Nesterov Gradient methods for minimizing composite objective function , 2007 .

[19]  S. Gadat,et al.  On the long time behavior of second order differential equations with asymptotically small dissipation , 2007, 0710.1107.

[20]  Ivan P. Gavrilyuk,et al.  Variational analysis in Sobolev and BV spaces , 2007, Math. Comput..

[21]  Marc Teboulle,et al.  A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems , 2009, SIAM J. Imaging Sci..

[22]  Sébastien Gadat,et al.  Second-order differential equations with asymptotically small dissipation and piecewise flat potentials , 2009 .

[23]  Heinz H. Bauschke,et al.  Convex Analysis and Monotone Operator Theory in Hilbert Spaces , 2011, CMS Books in Mathematics.

[24]  H. Attouch,et al.  A second-order differential system with hessian-driven damping; application to non-elastic shock laws , 2012 .

[25]  Dirk A. Lorenz,et al.  An Inertial Forward-Backward Algorithm for Monotone Inclusions , 2014, Journal of Mathematical Imaging and Vision.

[26]  Juan Peypouquet,et al.  A Dynamical Approach to an Inertial Forward-Backward Algorithm for Convex Minimization , 2014, SIAM J. Optim..

[27]  Benar Fux Svaiter,et al.  Newton-Like Dynamics and Forward-Backward Methods for Structured Monotone Inclusions in Hilbert Spaces , 2014, J. Optim. Theory Appl..

[28]  Gabriel Peyré,et al.  Activity Identification and Local Linear Convergence of Inertial Forward-Backward Splitting , 2015 .

[29]  J. Peypouquet Convex Optimization in Normed Spaces: Theory, Methods and Examples , 2015 .

[30]  Emmanuel J. Candès,et al.  Adaptive Restart for Accelerated Gradient Schemes , 2012, Foundations of Computational Mathematics.

[31]  A. Chambolle,et al.  On the convergence of the iterates of "FISTA" , 2015 .

[32]  Ramzi May Asymptotic for a second order evolution equation with convex potential and vanishing damping term , 2015, 1509.05598.

[33]  H. Attouch,et al.  Fast Convergence of an Inertial Gradient-like System with Vanishing Viscosity , 2015, 1507.04782.

[34]  Stephen P. Boyd,et al.  A Differential Equation for Modeling Nesterov's Accelerated Gradient Method: Theory and Insights , 2014, J. Mach. Learn. Res..

[35]  Mohamed-Jalal Fadili,et al.  Activity Identification and Local Linear Convergence of Forward-Backward-type Methods , 2015, SIAM J. Optim..

[36]  Juan Peypouquet,et al.  Fast convergence of inertial dynamics and algorithms with asymptotic vanishing viscosity , 2018, Math. Program..