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Persistent URL http://purl.org/net/epubs/work/54902
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Record Id 54902
Title On the evaluation complexity of composite function minimization with applications to nonconvex nonlinear programming
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
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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