Projects per year
Abstract
An adaptive regularization algorithm is proposed that uses Taylor models of the objective of order p, (Formula presented.), of the unconstrained objective function, and that is guaranteed to find a first- and second-order critical point in at most (Formula presented.) function and derivatives evaluations, where ε 1 and ε 1 are prescribed first- and second-order optimality tolerances. This is a simple algorithm and associated analysis compared to the much more general approach in Cartis et al. [Sharp worst-case evaluation complexity bounds for arbitrary-order nonconvex optimization with inexpensive constraints, arXiv:1811.01220, 2018] that addresses the complexity of criticality higher-than two; here, we use standard optimality conditions and practical subproblem solves to show a same-order sharp complexity bound for second-order criticality. Our approach also extends the method in Birgin et al. [Worst-case evaluation complexity for unconstrained nonlinear optimization using high-order regularized models, Math. Prog. A 163(1) (2017), pp. 359–368] to finding second-order critical points, under the same problem smoothness assumptions as were needed for first-order complexity.
Original language | English |
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Pages (from-to) | 243-256 |
Number of pages | 14 |
Journal | Optimization Methods and Software |
Volume | 35 |
Issue number | 2 |
DOIs | |
Publication status | Published - 3 Mar 2020 |
Keywords
- complexity analysis
- Nonconvex optimization
- regularization methods
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Projects
- 2 Active
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Complexity in nonlinear optimization
TOINT, P., Gould, N. I. M. & Cartis, C.
1/11/08 → …
Project: Research
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Activities
- 1 Invited talk
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Recent results in worst-case evaluation complexity for smooth and non-smooth, exact and inexact, nonconvex optimization
Philippe TOINT (Speaker)
8 May 2020Activity: Talk or presentation types › Invited talk