On the evaluation complexity of constrained nonlinear least-squares and general constrained nonlinear optimization using second-order methods
<p style="text-align:justify;"> 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 $\epsilon$ can be obtained by a second-order method using cub...
| Main Authors: | , , |
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| Format: | Journal article |
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Society for Industrial and Applied Mathematics
2015
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| _version_ | 1797106720060735488 |
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| author | Cartis, C Gould, N Toint, P |
| author_facet | Cartis, C Gould, N Toint, P |
| author_sort | Cartis, C |
| collection | OXFORD |
| description | <p style="text-align:justify;"> 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 $\epsilon$ can be obtained by a second-order method using cubic regularization in at most $O(\epsilon^{-3/2})$ 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 ($O(\epsilon^{-2})$) evaluation-complexity bound for solving general nonconvexly constrained optimization problems.</p> |
| first_indexed | 2024-03-07T07:06:30Z |
| format | Journal article |
| id | oxford-uuid:a3b3e54d-85c5-4732-a773-7145fa918e3a |
| institution | University of Oxford |
| last_indexed | 2024-03-07T07:06:30Z |
| publishDate | 2015 |
| publisher | Society for Industrial and Applied Mathematics |
| record_format | dspace |
| spelling | oxford-uuid:a3b3e54d-85c5-4732-a773-7145fa918e3a2022-05-09T13:39:23ZOn the evaluation complexity of constrained nonlinear least-squares and general constrained nonlinear optimization using second-order methodsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:a3b3e54d-85c5-4732-a773-7145fa918e3aSymplectic Elements at OxfordSociety for Industrial and Applied Mathematics2015Cartis, CGould, NToint, P <p style="text-align:justify;"> 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 $\epsilon$ can be obtained by a second-order method using cubic regularization in at most $O(\epsilon^{-3/2})$ 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 ($O(\epsilon^{-2})$) evaluation-complexity bound for solving general nonconvexly constrained optimization problems.</p> |
| spellingShingle | Cartis, C Gould, N Toint, P On the evaluation complexity of constrained nonlinear least-squares and general constrained nonlinear optimization using second-order methods |
| title | On the evaluation complexity of constrained nonlinear least-squares and general constrained nonlinear optimization using second-order methods |
| title_full | On the evaluation complexity of constrained nonlinear least-squares and general constrained nonlinear optimization using second-order methods |
| title_fullStr | On the evaluation complexity of constrained nonlinear least-squares and general constrained nonlinear optimization using second-order methods |
| title_full_unstemmed | On the evaluation complexity of constrained nonlinear least-squares and general constrained nonlinear optimization using second-order methods |
| title_short | On the evaluation complexity of constrained nonlinear least-squares and general constrained nonlinear optimization using second-order methods |
| title_sort | on the evaluation complexity of constrained nonlinear least squares and general constrained nonlinear optimization using second order methods |
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