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The exact information-based complexity of smooth convex minimization

Journal of Complexity (2016)


We obtain a new lower bound on the information-based complexity of first-order minimization of smooth and convex functions. We show that the bound matches the worst-case performance of the recently introduced Optimized Gradient Method (Drori and Teboulle, 2013; Kim and Fessler, 2015), thereby establishing that the bound is tight and can be realized by an efficient algorithm. The proof is based on a novel construction technique of smooth and convex functions.