Alternating Proximal Algorithms for Weakly Coupled Minimization Problems. Applications to Dynamical Games and PDE’s

By Hédy Attouch, Jérôme Bolte, Patrick Redont, Antoine Soubeyran. 2008

159 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/11931146d01e4a77311a39f3f1f22aed16bcb0d3

How researchers see this paper

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

1. Hédy Attouch
2. Jérôme Bolte
3. Lateef Olakunle Jolaoso
4. Juan Peypouquet
5. Qiao-Li Dong
6. Oluwatosin Temitope Mewomo
7. Adeolu Taiwo
8. Timilehin Opeyemi Alakoya

Citations in the corpus

• Proximal Alternating Minimization and Projection Methods for Nonconvex Problems: An Approach Based on the Kurdyka-Lojasiewicz Inequality (2008, methodology): “Secondly, we rely on a new class of alternating minimization algorithms with costs to move which has recently been introduced in [6] (see also [7]) and which has proved to be a flexible tool [5] permitting to handle general coupling functions Q(x, y) (for example Q(x, y) = ‖Ax−By‖2, with A, B linear”
• Solving the split equality problem without prior knowledge of operator norms (2015, background): “Algorithms for solving the SEP receive great attention; see, for instance, [1,2,4,5,8,9].”
• A unified algorithm for solving variational inequality and fixed point problems with application to the split equality problem (2019, background): “…by Censor and Elfving (1994) and defined as find x ∈ C such that Ax ∈ Q. (4.2) The SEP (4.1) covers many situations, such as for instance in domain decomposition for PDE’s, game theory and intensity-modulated radiation therapy (IMRT) (Attouch et al. 2008; Censor et al. 2006; Moudafi 2014).”
• Convex Optimization in Normed Spaces: Theory, Methods and Examples (2015, background): “Alternating variants have been studied in [8], [11], [14], among others.”
• Convergence of descent methods for semi-algebraic and tame problems: proximal algorithms, forward–backward splitting, and regularized Gauss–Seidel methods (2013, background): “Observe that this result is new even in the context of convex optimization where this problem was considered first (see the seminal work [8] and the recent study [4]).”
• Asymptotic behavior of coupled dynamical systems with multiscale aspects (2009, unknown): “For the cognitive and psychological interpretation of the costs to move terms ‖ ξ − x1,k ‖ 2 X1 and ‖ η − x2,k ‖ 2 X2 consult [3], [4], [7].”
• ASYMPTOTIC BEHAVIOR OF SECOND-ORDER DISSIPATIVE EVOLUTION EQUATIONS COMBINING POTENTIAL WITH NON-POTENTIAL EFFECTS ∗ (2009, background): “In decision sciences, they reflect some aspects of agents behaviors like anchoring and inertia, and can be interpreted as “low local costs to change”, see [11,15].”
• Solving split equality fixed-point problem of quasi-nonexpansive mappings without prior knowledge of operators norms (2015, background): “In decision sciences, this allows to consider agents who interplay only via some components of their decision variables (see [13]).”
• Convex Optimization in Normed Spaces (2015, background): “Alternating variants have been studied in [8], [11], [14], among others.”