Name
Title | ||
|---|---|---|
Smoothing projected Barzilai–Borwein method for constrained non-Lipschitz optimization |
Abstract | ||
|---|---|---|
We 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 $$\\ell _2$$ℓ2-$$\\ell _p$$ℓp problems, image restoration problems, and stochastic linear complementarity problems show that the SPBB algorithm is promising. |
Year | DOI | Venue |
|---|---|---|
2016 | https://doi.org/10.1007/s10589-016-9854-9 | Computational Optimization and Applications |
Keywords | Field | DocType |
Smoothing projected Barzilai–Borwein algorithm,Constrained non-Lipschitz optimization,Nonsmooth nonconvex optimization,Smoothing approximation,\(\ell _2\),-,\(\ell _p\),problem,Image restoration,Stochastic linear complementarity problem | Convergence (routing),Mathematical optimization,Mathematical analysis,Convex set,Minification,Smoothing,Stationary point,Lipschitz continuity,Image restoration,Limit point,Mathematics | Journal |
Volume | Issue | ISSN |
65 | 3 | 0926-6003 |
Citations | PageRank | References |
1 | 0.35 | 28 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Yakui Huang | 1 | 30 | 4.96 |
| Hongwei Liu | 2 | 78 | 12.29 |