Inertial proximal alternating minimization for nonconvex and nonsmooth problems
Abstract In this paper, we study the minimization problem of the type L ( x , y ) = f ( x ) + R ( x , y ) + g ( y ) $L(x,y)=f(x)+R(x,y)+g(y)$ , 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 wit...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2017-09-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13660-017-1504-y |
| _version_ | 1818155161597509632 |
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| author | Yaxuan Zhang Songnian He |
| author_facet | Yaxuan Zhang Songnian He |
| author_sort | Yaxuan Zhang |
| collection | DOAJ |
| description | Abstract In this paper, we study the minimization problem of the type L ( x , y ) = f ( x ) + R ( x , y ) + g ( y ) $L(x,y)=f(x)+R(x,y)+g(y)$ , 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. |
| first_indexed | 2024-12-11T14:38:00Z |
| format | Article |
| id | doaj.art-8ed5ed3df7024623850fc619ac35819c |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-12-11T14:38:00Z |
| publishDate | 2017-09-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-8ed5ed3df7024623850fc619ac35819c2022-12-22T01:02:05ZengSpringerOpenJournal of Inequalities and Applications1029-242X2017-09-012017111310.1186/s13660-017-1504-yInertial proximal alternating minimization for nonconvex and nonsmooth problemsYaxuan Zhang0Songnian He1College of Science, Civil Aviation University of ChinaCollege of Science, Civil Aviation University of ChinaAbstract In this paper, we study the minimization problem of the type L ( x , y ) = f ( x ) + R ( x , y ) + g ( y ) $L(x,y)=f(x)+R(x,y)+g(y)$ , 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.http://link.springer.com/article/10.1186/s13660-017-1504-ynonconvex nonsmooth optimizationproximal alternating minimizationinertialKurdyka-Lojasiewicz inequalityconvergence |
| spellingShingle | Yaxuan Zhang Songnian He Inertial proximal alternating minimization for nonconvex and nonsmooth problems Journal of Inequalities and Applications nonconvex nonsmooth optimization proximal alternating minimization inertial Kurdyka-Lojasiewicz inequality convergence |
| title | Inertial proximal alternating minimization for nonconvex and nonsmooth problems |
| title_full | Inertial proximal alternating minimization for nonconvex and nonsmooth problems |
| title_fullStr | Inertial proximal alternating minimization for nonconvex and nonsmooth problems |
| title_full_unstemmed | Inertial proximal alternating minimization for nonconvex and nonsmooth problems |
| title_short | Inertial proximal alternating minimization for nonconvex and nonsmooth problems |
| title_sort | inertial proximal alternating minimization for nonconvex and nonsmooth problems |
| topic | nonconvex nonsmooth optimization proximal alternating minimization inertial Kurdyka-Lojasiewicz inequality convergence |
| url | http://link.springer.com/article/10.1186/s13660-017-1504-y |
| work_keys_str_mv | AT yaxuanzhang inertialproximalalternatingminimizationfornonconvexandnonsmoothproblems AT songnianhe inertialproximalalternatingminimizationfornonconvexandnonsmoothproblems |