Complexity of a projected Newton-CG method for optimization with bounds
This paper describes a method for solving smooth nonconvex minimization problems subject to bound constraints with good worst-case complexity guarantees and practical performance. The method contains elements of two existing methods: the classical gradient projection approach for bound-constrained o...
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| Vydané v: | Mathematical programming Ročník 207; číslo 1-2; s. 107 - 144 |
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| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.09.2024
Springer |
| Predmet: | |
| ISSN: | 0025-5610, 1436-4646 |
| On-line prístup: | Získať plný text |
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| Shrnutí: | This paper describes a method for solving smooth nonconvex minimization problems subject to bound constraints with good worst-case complexity guarantees 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. |
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| ISSN: | 0025-5610 1436-4646 |
| DOI: | 10.1007/s10107-023-02000-z |