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Persistent URL
http://purl.org/net/epubs/work/54902
Record Status
Checked
Record Id
54902
Title
On the evaluation complexity of composite function minimization with applications to nonconvex nonlinear programming
Contributors
C Cartis (Edinburgh U.)
,
NIM Gould (STFC Rutherford Appleton Lab.)
,
PL Toint (Facultes Universitaires de la Paix)
Abstract
We estimate the worst-case complexity of minimizing an unconstrained, nonconvex composite objective with a structured nonsmooth term by means of some first-order methods. We find that it is unaffected by the nonsmoothness of the objective in that a first-order trust-region or quadratic regularization method applied to it takes at most O(epsilon−2) functionevaluations to reduce the size of a first-order criticality measure below epsilon. Specializing this result to the case when the composite objective is an exact penalty function allows us to consider the objective- and constraint-evaluation worst-case complexity of nonconvex equality-constrained optimization when the solution is computed using a first-order exact penalty method. We obtain that in the reasonable case when the penalty parameters are bounded, the complexity of reaching within epsilon of a KKT point is at most O(epsilon−2) problem-evaluations, which is the same in order as the function-evaluation complexity of steepest-descent methods applied to unconstrained, nonconvex smooth optimization.
Organisation
CSE
,
CSE-NAG
,
STFC
Keywords
Funding Information
Related Research Object(s):
Licence Information:
Language
English (EN)
Type
Details
URI(s)
Local file(s)
Year
Report
RAL Technical Reports
RAL-TR-2011-005. 2011.
RAL-TR-2011-005.pdf
2011
Journal Article
SIAM J Optimiz
21, no. 4 (2011): 1721-1739.
doi:10.1137/11082381X
2011
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