A forward-backward penalty scheme with inertial effects for monotone inclusions. Applications to convex bilevel programming

We investigate a forward-backward splitting algorithm of penalty type with inertial effects for finding the zeros of the sum of a maximally monotone operator and a cocoercive one and the convex normal cone to the set of zeroes of an another cocoercive operator. Weak ergodic convergence is obtained f...

Celý popis

Uloženo v:
Podrobná bibliografie
Vydáno v:Optimization Ročník 68; číslo 10; s. 1855 - 1880
Hlavní autoři: Boţ, Radu Ioan, Nguyen, Dang-Khoa
Médium: Journal Article
Jazyk:angličtina
Vydáno: England Taylor & Francis 03.10.2019
Taylor & Francis LLC
Témata:
Algorithms
Convergence
convex bilevel optimization
Ergodic processes
Fitzpatrick function
forward-backward splitting algorithm
Inclusions
Maximally monotone operator
Operators (mathematics)
Maximally monotone operator
65K05
convex bilevel optimization
forward–backward splitting algorithm
Fitzpatrick function
90C25
47H05
ISSN:0233-1934, 1029-4945, 1029-4945
On-line přístup:Získat plný text
Tagy: Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
Popis
Shrnutí:We investigate a forward-backward splitting algorithm of penalty type with inertial effects for finding the zeros of the sum of a maximally monotone operator and a cocoercive one and the convex normal cone to the set of zeroes of an another cocoercive operator. Weak ergodic convergence is obtained for the iterates, provided that a condition expressed via the Fitzpatrick function of the operator describing the underlying set of the normal cone is verified. Under strong monotonicity assumptions, strong convergence for the sequence of generated iterates is proved. As a particular instance we consider a convex bilevel minimization problem including the sum of a non-smooth and a smooth function in the upper level and another smooth function in the lower level. We show that in this context weak non-ergodic and strong convergence can be also achieved under inf-compactness assumptions for the involved functions.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
content type line 23
ISSN:0233-1934
1029-4945
1029-4945
DOI:10.1080/02331934.2018.1556662