Dynamical systems and forward–backward algorithms associated with the sum of a convex subdifferential and a monotone cocoercive operator
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Publication:3453400
DOI10.1080/02331934.2014.971412zbMath1345.34115arXiv1403.6312OpenAlexW2059425302MaRDI QIDQ3453400
Publication date: 27 November 2015
Published in: Optimization (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1403.6312
dissipative dynamicsLyapunov analysisforward-backward algorithmsLevenberg-Marquardt regularizationmultiobjective decisionweak asymptotic convergencestructured monotone inclusionsproximal-gradient methodsubdifferential operators, cocoercive operators
Methods of quasi-Newton type (90C53) Iterative procedures involving nonlinear operators (47J25) Numerical methods based on nonlinear programming (49M37) Evolution inclusions (34G25)
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Cites Work
- A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
- Global convergence of a closed-loop regularized Newton method for solving monotone inclusions in Hilbert spaces
- A continuous gradient-like dynamical approach to Pareto-optimization in Hilbert spaces
- Continuous gradient projection method in Hilbert spaces
- Strong asymptotic convergence of evolution equations governed by maximal monotone operators with Tikhonov regularization
- Asymptotic convergence of nonlinear contraction semigroups in Hilbert space
- Quelques propriétés des opérateurs angle-bornes et n-cycliquement monotones
- Un exemple concernant le comportement asymptotique de la solution du problème \(du/dt+\partial\varphi(\mu)\ni=0\)
- A dynamical approach to convex minimization coupling approximation with the steepest descent method
- 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
- Asymptotic behavior of coupled dynamical systems with multiscale aspects
- A Continuous Dynamical Newton-Like Approach to Solving Monotone Inclusions
- A Parallel Splitting Method for Coupled Monotone Inclusions
- Asymptotic behavior of second-order dissipative evolution equations combining potential with non-potential effects
- Coupling Forward-Backward with Penalty Schemes and Parallel Splitting for Constrained Variational Inequalities
- Splitting Algorithms for the Sum of Two Nonlinear Operators
- Solving monotone inclusions via compositions of nonexpansive averaged operators
- A Dynamical Approach to an Inertial Forward-Backward Algorithm for Convex Minimization
- The steepest descent dynamical system with control. Applications to constrained minimization
- Weak convergence of the sequence of successive approximations for nonexpansive mappings
- Convex analysis and monotone operator theory in Hilbert spaces
- A convergence result for nonautonomous subgradient evolution equations and its application to the steepest descent exponential penalty trajectory in linear programming