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- W4287251441 abstract "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 $epsilon$ (which is compared with related definitions from previous works), we derive complexity bounds in terms of $epsilon$ 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." @default.
- W4287251441 created "2022-07-25" @default.
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- W4287251441 date "2021-03-29" @default.
- W4287251441 modified "2023-09-28" @default.
- W4287251441 title "Complexity of a Projected Newton-CG Method for Optimization with Bounds" @default.
- W4287251441 doi "https://doi.org/10.48550/arxiv.2103.15989" @default.
- W4287251441 hasPublicationYear "2021" @default.
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