Research output per year
Research output per year
Coralia Cartis, Nicholas I M Gould, Philippe L. Toint
Research output: Contribution to journal › Article › peer-review
When solving the general smooth nonlinear and possibly nonconvex optimization problem involving equality and/or inequality constraints, an approximate first-order critical point of accuracy ∈ can be obtained by a second-order method using cubic regularization in at most O(∈<sup>-3/2</sup> ) evaluations of problem functions, the same order bound as in the unconstrained case. This result is obtained by first showing that the same result holds for inequality constrained nonlinear least-squares. As a consequence, the presence of (possibly nonconvex) equality/inequality constraints does not affect the complexity of finding approximate first-order critical points in nonconvex optimization. This result improves on the best known (O(∈<sup>-2</sup> )) evaluation-complexity bound for solving general nonconvexly constrained optimization problems.
Original language | English |
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Pages (from-to) | 836-851 |
Number of pages | 16 |
Journal | SIAM Journal on Numerical Analysis |
Volume | 53 |
Issue number | 2 |
DOIs | |
Publication status | Published - 2015 |
Research output: Book/Report/Journal › Book
Research output: Contribution to journal › Article › peer-review
Research output: Contribution in Book/Catalog/Report/Conference proceeding › Chapter
TOINT, P., Gould, N. I. M. & Cartis, C.
1/11/08 → …
Project: Research
Philippe Toint (Speaker)
Activity: Talk or presentation types › Invited talk
Philippe Toint (Invited speaker)
Activity: Talk or presentation types › Oral presentation
Philippe Toint (Speaker)
Activity: Talk or presentation types › Oral presentation