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DOI 10.5286/raltr.2009006
Persistent URL http://purl.org/net/epubs/work/56166
Record Status Checked
Record Id 56166
Title An adaptive cubic regularization algorithm for nonconvex optimization with convex constraints and its function-evaluation complexity
Abstract The adaptive cubic overestimation algorithm described by Cartis, Gould and Toint (RAL-TR- 2007-007) is adapted to the problem of minimizing a nonlinear, possibly nonconvex, smooth objective function over a convex domain. Convergence to first-order critical points is shown under standard assumptions, but without any Lipschitz continuity requirement on the objective?s Hessian. A worst-case complexity analysis in terms of evaluations of the problem?s function and derivatives is also presented for the Lipschitz continuous case and for a variant of the resulting algorithm. This analysis extends the best known bound for general unconstrained problems to nonlinear problems with convex constraints.
Organisation CSE , CSE-NAG , STFC
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Language English (EN)
Type Details URI(s) Local file(s) Year
Report RAL Technical Reports RAL-TR-2009-006. STFC, 2009. cgtRALTR2009006.pdf 2009