Convergence Results of a New Monotone Inertial Forward–Backward Splitting Algorithm Under the Local Hölder Error Bound Condition

In this paper, we introduce a new monotone inertial Forward–Backward splitting algorithm (newMIFBS) for the convex minimization of the sum of a non-smooth function and a smooth differentiable function. The newMIFBS can overcome two negative effects caused by IFBS, i.e., the undesirable oscillations...

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Bibliographic Details
Published in:Applied mathematics & optimization Vol. 85; no. 2
Main Authors: Wang, Ting, Liu, Hongwei
Format: Journal Article
Language:English
Published: New York Springer US 01.04.2022
Springer Nature B.V
Subjects:
Algorithms
Calculus of Variations and Optimal Control; Optimization
Control
Convergence
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Numerical and Computational Physics
Simulation
Splitting
Systems Theory
Theoretical
Local hölder error bound condition
94A08
90C25
Monotone Inertial Forward–Backward Splitting algorithm
65K10
Rate of convergence
94A12
Optimization
ISSN:0095-4616, 1432-0606
Online Access:Get full text
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Summary:In this paper, we introduce a new monotone inertial Forward–Backward splitting algorithm (newMIFBS) for the convex minimization of the sum of a non-smooth function and a smooth differentiable function. The newMIFBS can overcome two negative effects caused by IFBS, i.e., the undesirable oscillations ultimately and extremely nonmonotone, which might lead to the algorithm diverges, for some special problems. We study the improved convergence rates for the objective function and the convergence of iterates under a local Hölder error bound (Local HEB) condition. Also, our study extends the previous results for IFBS under the Local HEB. Finally, we present some numerical experiments for the simplest newMIFBS (hybrid_MIFBS) to illustrate our results.
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ISSN:0095-4616
1432-0606
DOI:10.1007/s00245-022-09859-y