Smoothing projected Barzilai-Borwein method for constrained non-Lipschitz optimization
Huang, Yakui1,2; Liu, Hongwei1
AbstractWe present a smoothing projected Barzilai-Borwein (SPBB) algorithm for solving a class of minimization problems on a closed convex set, where the objective function is nonsmooth nonconvex, perhaps even non-Lipschitz. At each iteration, the SPBB algorithm applies the projected gradient strategy that alternately uses the two Barzilai-Borwein stepsizes to the smooth approximation of the original problem. Nonmonotone scheme is adopted to ensure global convergence. Under mild conditions, we prove convergence of the SPBB algorithm to a scaled stationary point of the original problem. When the objective function is locally Lipschitz continuous, we consider a general constrained optimization problem and show that any accumulation point generated by the SPBB algorithm is a stationary point associated with the smoothing function used in the algorithm. Numerical experiments on - problems, image restoration problems, and stochastic linear complementarity problems show that the SPBB algorithm is promising.
KeywordSmoothing projected Barzilai-Borwein algorithm Constrained non-Lipschitz optimization Nonsmooth nonconvex optimization Smoothing approximation l(2)-l(p) problem Image restoration Stochastic linear complementarity problem
Funding ProjectNational Natural Science Foundation of China (NNSFC)[61072144] ; National Natural Science Foundation of China (NNSFC)[61179040] ; Fundamental Research Funds for the Central Universities[K50513100007]
WOS Research AreaOperations Research & Management Science ; Mathematics
WOS SubjectOperations Research & Management Science ; Mathematics, Applied
WOS IDWOS:000387773500005
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Document Type期刊论文
Corresponding AuthorHuang, Yakui
Affiliation1.Xidian Univ, Sch Math & Stat, Xian 710126, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, ICMSEC, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Huang, Yakui,Liu, Hongwei. Smoothing projected Barzilai-Borwein method for constrained non-Lipschitz optimization[J]. COMPUTATIONAL OPTIMIZATION AND APPLICATIONS,2016,65(3):671-698.
APA Huang, Yakui,&Liu, Hongwei.(2016).Smoothing projected Barzilai-Borwein method for constrained non-Lipschitz optimization.COMPUTATIONAL OPTIMIZATION AND APPLICATIONS,65(3),671-698.
MLA Huang, Yakui,et al."Smoothing projected Barzilai-Borwein method for constrained non-Lipschitz optimization".COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 65.3(2016):671-698.
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