Convergence of a Relaxed Inertial Forward–Backward Algorithm for Structured Monotone Inclusions

In a Hilbert space H , we study the convergence properties of a class of relaxed inertial forward–backward algorithms. They aim to solve structured monotone inclusions of the form A x + B x ∋ 0 where A : H → 2 H is a maximally monotone operator and B : H → H is a cocoercive operator. We extend to th...

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Vydané v:Applied mathematics & optimization Ročník 80; číslo 3; s. 547 - 598
Hlavní autori: Attouch, Hedy, Cabot, Alexandre
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York Springer US 01.12.2019
Springer Nature B.V
Springer Verlag (Germany)
Predmet:
Acceleration
Algorithms
Calculus of Variations and Optimal Control; Optimization
Control
Convergence
Game theory
Hilbert space
Inclusions
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Numerical and Computational Physics
Simulation
Systems Theory
Theoretical
Relaxation
65K05
Inertial forward–backward algorithms
Inertial Krasnoselskii–Mann iteration
90C25
Nash equilibration
Structured monotone inclusions
Convergence rate
65K10
49M37
Cocoercive operators
Forward backward algorithm
extragradient
Proximal-gradient method
Monotone inclusion
nonconvex
operators
convergence
convex minimization
iteration-complexity
splitting method
sum
proximal point algorithm
ISSN:0095-4616, 1432-0606
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Popis
Shrnutí:In a Hilbert space H , we study the convergence properties of a class of relaxed inertial forward–backward algorithms. They aim to solve structured monotone inclusions of the form A x + B x ∋ 0 where A : H → 2 H is a maximally monotone operator and B : H → H is a cocoercive operator. We extend to this class of problems the acceleration techniques initially introduced by Nesterov, then developed by Beck and Teboulle in the case of structured convex minimization (FISTA). As an important element of our approach, we develop an inertial and parametric version of the Krasnoselskii–Mann theorem, where joint adjustment of the inertia and relaxation parameters plays a central role. This study comes as a natural extension of the techniques introduced by the authors for the study of relaxed inertial proximal algorithms. An illustration is given to the inertial Nash equilibration of a game combining non-cooperative and cooperative aspects.
Bibliografia:ObjectType-Article-1
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content type line 14
ISSN:0095-4616
1432-0606
DOI:10.1007/s00245-019-09584-z