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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Vydáno v:Mathematical programming Ročník 207; číslo 1-2; s. 107 - 144
Hlavní autoři: Xie, Yue, Wright, Stephen J.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2024
Springer
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ISSN:0025-5610, 1436-4646
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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.
ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-023-02000-z