Worst case complexity of direct search under convexity
نویسندگان
چکیده
منابع مشابه
Worst case complexity of direct search under convexity
In this paper we prove that the broad class of direct-search methods of directional type, based on imposing sufficient decrease to accept new iterates, exhibits the same worst case complexity bound and global rate of the gradient method for the unconstrained minimization of a convex and smooth function. More precisely, it will be shown that the number of iterations needed to reduce the norm of ...
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In this paper we prove that the broad class of direct-search methods of directional type based on imposing sufficient decrease to accept new iterates shares the worst case complexity bound of steepest descent for the unconstrained minimization of a smooth function, more precisely that the number of iterations needed to reduce the norm of the gradient of the objective function below a certain th...
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The worst case complexity of direct-search methods has been recently analyzed when they use positive spanning sets and impose a sufficient decrease condition to accept new iterates. Assuming that the objective function is smooth, it is now known that such methods require at most O(n −2) function evaluations to compute a gradient of norm below ∈ (0, 1), where n is the dimension of the problem. S...
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ژورنال
عنوان ژورنال: Mathematical Programming
سال: 2014
ISSN: 0025-5610,1436-4646
DOI: 10.1007/s10107-014-0847-0