Smooth strongly convex interpolation and exact worst-case performance of first-order methods
نویسندگان
چکیده
منابع مشابه
Smooth strongly convex interpolation and exact worst-case performance of first-order methods
We show that the exact worst-case performance of fixed-step first-order methods for unconstrained optimization of smooth (possibly strongly) convex functions can be obtained by solving convex programs. Finding the worst-case performance of a black-box first-order method is formulated as an optimization problem over a set of smooth (strongly) convex functions and initial conditions. We develop c...
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The usual approach to developing and analyzing first-order methods for smooth convex optimization assumes that the gradient of the objective function is uniformly smooth with some Lipschitz constant L. However, in many settings the differentiable convex function f(·) is not uniformly smooth – for example in D-optimal design where f(x) := − ln det(HXH ), or even the univariate setting with f(x) ...
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ژورنال
عنوان ژورنال: Mathematical Programming
سال: 2016
ISSN: 0025-5610,1436-4646
DOI: 10.1007/s10107-016-1009-3