Approaching nonsmooth nonconvex minimization through second-order proximal-gradient dynamical systems
From MaRDI portal
Publication:1991713
DOI10.1007/s00028-018-0441-7zbMath1402.34069arXiv1711.06570OpenAlexW2963178522WikidataQ130191296 ScholiaQ130191296MaRDI QIDQ1991713
Szilárd Csaba László, Ernö Robert Csetnek, Radu Ioan Boţ
Publication date: 30 October 2018
Published in: Journal of Evolution Equations (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1711.06570
limiting subdifferentialnonsmooth nonconvex optimizationKurdyka-Łojasiewicz propertysecond-order dynamical system
Nonconvex programming, global optimization (90C26) Nonlinear programming (90C30) Monotone operators and generalizations (47H05) Iterative procedures involving nonlinear operators (47J25) Nonlinear differential equations in abstract spaces (34G20) Asymptotic properties of solutions to ordinary differential equations (34D05)
Related Items
Fast convex optimization via inertial dynamics combining viscous and Hessian-driven damping with time rescaling ⋮ Continuous dynamics related to monotone inclusions and non-smooth optimization problems ⋮ A forward-backward dynamical approach for nonsmooth problems with block structure coupled by a smooth function ⋮ A gradient-type algorithm with backward inertial steps associated to a nonconvex minimization problem ⋮ A new minimizing-movements scheme for curves of maximal slope ⋮ Fast optimization via inertial dynamics with closed-loop damping ⋮ An extension of the second order dynamical system that models Nesterov's convex gradient method ⋮ Convergence rates for an inertial algorithm of gradient type associated to a smooth non-convex minimization ⋮ Asymptotic analysis of a structure-preserving integrator for damped Hamiltonian systems ⋮ A second-order dynamical approach with variable damping to nonconvex smooth minimization ⋮ Convergence rates for the heavy-ball continuous dynamics for non-convex optimization, under Polyak-Łojasiewicz condition ⋮ Two structure-preserving time discretizations for gradient flows
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- An inertial forward-backward algorithm for the minimization of the sum of two nonconvex functions
- Proximal alternating linearized minimization for nonconvex and nonsmooth problems
- A dynamical system associated with the fixed points set of a nonexpansive operator
- Continuous gradient projection method in Hilbert spaces
- Approaching the solving of constrained variational inequalities via penalty term-based dynamical systems
- On the convergence of the proximal algorithm for nonsmooth functions involving analytic features
- Convergence of solutions to second-order gradient-like systems with analytic nonlinearities
- On gradients of functions definable in o-minimal structures
- A second-order gradient-like dissipative dynamical system with Hessian-driven damping. Application to optimization and mechanics.
- Convergence of descent methods for semi-algebraic and tame problems: proximal algorithms, forward-backward splitting, and regularized Gauss-Seidel methods
- Newton-like dynamics and forward-backward methods for structured monotone inclusions in Hilbert spaces
- Convergence rates for forward-backward dynamical systems associated with strongly monotone inclusions
- Second Order Forward-Backward Dynamical Systems For Monotone Inclusion Problems
- A dynamic approach to a proximal-Newton method for monotone inclusions in Hilbert spaces, with complexity O(1/n^2)
- iPiano: Inertial Proximal Algorithm for Nonconvex Optimization
- Variational Analysis in Sobolev and BV Spaces
- The Convergence Problem for Dissipative Autonomous Systems
- A Continuous Dynamical Newton-Like Approach to Solving Monotone Inclusions
- Proximal Alternating Minimization and Projection Methods for Nonconvex Problems: An Approach Based on the Kurdyka-Łojasiewicz Inequality
- Dynamical systems and forward–backward algorithms associated with the sum of a convex subdifferential and a monotone cocoercive operator
- Clarke Subgradients of Stratifiable Functions
- Characterizations of Łojasiewicz inequalities: Subgradient flows, talweg, convexity
- Variational Analysis
- On the Minimizing Property of a Second Order Dissipative System in Hilbert Spaces
- 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
- Weak Convergence of a Relaxed and Inertial Hybrid Projection-Proximal Point Algorithm for Maximal Monotone Operators in Hilbert Space
- Variational Analysis and Generalized Differentiation I
- The Łojasiewicz Inequality for Nonsmooth Subanalytic Functions with Applications to Subgradient Dynamical Systems
- An inertial proximal method for maximal monotone operators via discretization of a nonlinear oscillator with damping
