On the evaluation complexity of constrained nonlinear least-squares and general constrained nonlinear optimnization using second-order methods

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Persistent URL	http://purl.org/net/epubs/work/65243
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Record Id	65243
Title	On the evaluation complexity of constrained nonlinear least-squares and general constrained nonlinear optimnization using second-order methods
Contributors	C Cartis, NIM Gould (STFC Rutherford Appleton Lab.), PL Toint
Abstract	When solving the general smooth nonlinear optimization problem involving equality and/or inequality constraints, an approximate first-order critical point of accuracy e can be obtained by a second-order method using cubic regularization in at most O(e−3/2) problem- functions evaluations, 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 nonlinear) 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(e−2)) evaluation- complexity bound for solving general nonconvexly constrained optimization problems.
Organisation	STFC , SCI-COMP , SCI-COMP-CM
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Related Research Object(s):	18469665
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Language	English (EN)

Type	Details	URI(s)	Local file(s)	Year
Report	RAL Preprints RAL-P-2013-002. 2013.		RAL-P-2013-002.pdf	2013