File Download
There are no files associated with this item.
Supplementary
-
Citations:
- Appears in Collections:
Article: Complexity of a Projected Newton-CG Method for Optimization with Bounds
Title | Complexity of a Projected Newton-CG Method for Optimization with Bounds |
---|---|
Authors | |
Issue Date | 2022 |
Citation | ArXiv, 2022 How to Cite? |
Abstract | This paper describes a method for solving smooth nonconvex minimization problems subject to bound constraints with good worst-case complexity and practical performance. The method contains elements of two existing methods: the classical gradient projection approach for bound-constrained optimization and a recently proposed Newton-conjugate gradient algorithm for unconstrained nonconvex optimization. Using a new definition of approximate second-order optimality parametrized by some tolerance ϵ (which is compared with related definitions from previous works), we derive complexity bounds in terms of ϵ for both the number of iterations required and the total amount of computation. The latter is measured by the number of gradient evaluations or Hessian-vector products. We also describe illustrative computational results on several test problems from low-rank matrix optimization. |
Persistent Identifier | http://hdl.handle.net/10722/319212 |
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Xie, Y | - |
dc.contributor.author | Wright, STEPHEN | - |
dc.date.accessioned | 2022-10-14T05:09:10Z | - |
dc.date.available | 2022-10-14T05:09:10Z | - |
dc.date.issued | 2022 | - |
dc.identifier.citation | ArXiv, 2022 | - |
dc.identifier.uri | http://hdl.handle.net/10722/319212 | - |
dc.description.abstract | This paper describes a method for solving smooth nonconvex minimization problems subject to bound constraints with good worst-case complexity and practical performance. The method contains elements of two existing methods: the classical gradient projection approach for bound-constrained optimization and a recently proposed Newton-conjugate gradient algorithm for unconstrained nonconvex optimization. Using a new definition of approximate second-order optimality parametrized by some tolerance ϵ (which is compared with related definitions from previous works), we derive complexity bounds in terms of ϵ for both the number of iterations required and the total amount of computation. The latter is measured by the number of gradient evaluations or Hessian-vector products. We also describe illustrative computational results on several test problems from low-rank matrix optimization. | - |
dc.language | eng | - |
dc.relation.ispartof | ArXiv | - |
dc.title | Complexity of a Projected Newton-CG Method for Optimization with Bounds | - |
dc.type | Article | - |
dc.identifier.email | Xie, Y: yxie21@hku.hk | - |
dc.identifier.authority | Xie, Y=rp02906 | - |
dc.identifier.doi | 10.48550/arXiv.2103.15989 | - |
dc.identifier.hkuros | 338567 | - |