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\iteman{io-port 06104813}
\itemau{Cartis, C.; Gould, N.I.M.; Toint, Ph.L.}
\itemti{An adaptive cubic regularization algorithm for nonconvex optimization with convex constraints and its function-evaluation complexity.}
\itemso{IMA J. Numer. Anal. 32, No. 4, 1662-1695 (2012).}
\itemab
Summary: The adaptive cubic regularization algorithm described in Cartis et al. (2009, Adaptive cubic regularisation methods for unconstrained optimization. Part I: motivation, convergence and numerical results. Math. Program., 127, 245-295; 2010, Adaptive cubic regularisation methods for unconstrained optimization. Part II: worst-case function- and derivative-evaluation complexity [online]. Math. Program., DOI: 10.1007/s10107-009-0337-y) 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, 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.
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\itemcc{}
\itemut{nonlinear optimization; convex constraints; cubic regularization/regularization; numerical algorithms; global convergence; worst-case complexity}
\itemli{doi:10.1093/imanum/drr035}
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