Inertial proximal alternating minimization for nonconvex and nonsmooth problems

In this paper, we study the minimization problem of the type L ( x , y ) = f ( x ) + R ( x , y ) + g ( y ) , where f and g are both nonconvex nonsmooth functions, and R is a smooth function we can choose. We present a proximal alternating minimization algorithm with inertial effect. We obtain the co...

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Bibliographic Details
Published in:Journal of inequalities and applications Vol. 2017; no. 1; pp. 232 - 13
Main Authors: Zhang, Yaxuan, He, Songnian
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 2017
Springer Nature B.V
SpringerOpen
Subjects:
Analysis
Applications of Mathematics
Convergence
Critical point
inertial
Kurdyka-Lojasiewicz inequality
Mathematics
Mathematics and Statistics
nonconvex nonsmooth optimization
Optimization
proximal alternating minimization
Kurdyka-Lojasiewicz inequality
convergence
inertial
proximal alternating minimization
nonconvex nonsmooth optimization
ISSN:1029-242X, 1025-5834, 1029-242X
Online Access:Get full text
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Summary:In this paper, we study the minimization problem of the type L ( x , y ) = f ( x ) + R ( x , y ) + g ( y ) , where f and g are both nonconvex nonsmooth functions, and R is a smooth function we can choose. We present a proximal alternating minimization algorithm with inertial effect. We obtain the convergence by constructing a key function H that guarantees a sufficient decrease property of the iterates. In fact, we prove that if H satisfies the Kurdyka-Lojasiewicz inequality, then every bounded sequence generated by the algorithm converges strongly to a critical point of L .
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ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-017-1504-y