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...
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| Format: | Journal article |
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Society for Industrial and Applied Mathematics
2015
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| Summary: | <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> |
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