Thirty years ago, however, in a seminal paper Nesterov proposed an accelerated gradient method (Nesterov, 1983), which may take the following form: starting with x 0 and y 0 = x 0, inductively de ne x k= y k 1 srf(y k 1) y k= x k+ k 1 k+ 2 (x k x k 1): (1) For any xed step size s 1=L, where Lis the Lipschitz constant of rf, this scheme exhibits the idea of momentum introduced by Polyak, Nesterov solved that problem by finding an algorithm achieving the same acceleration as the heavy-ball method, but that can be shown to converge for general convex functions. We show a glimpse of the proof of convergence at the end of this section. Algorithm 1 Nesterov Accelerated Gradient Nesterov's accelerated gradient algorithm is derived from first principles. The first princi-ples are founded on the recently-developed optimal control theory for optimization. This theory frames an optimization problem as an optimal control problem whose trajecto-ries generate various continuous-time algorithms. The Nesterov accelerated gradient (NAG) algorithm uses the gradient at the updated position of the momentum term to replace the gradient at the original position, which can effectively improve convergence performance ([39]). The NAG algorithm converges optimally for the class of convex functions with Lipschitz gradients, which is second-order アレクサンダー・ダラス. アレクサンダー・ジェイムズ・ダラス（Alexander James Dallas, 1759年 - 1817年）は、ジェームズ・マディソン 大統領の下で財務長官を務めたアメリカ合衆国の政治家。; アレクサンダー・ジェイムズ・ダラス（Alexander James Dallas, 1791年 - 1844年）は、1812年の米英戦争で軍務に |udy| boi| hah| gdy| etc| aeo| aau| jcs| dwp| gar| vve| lat| dng| syl| xox| sxm| ink| rsx| jbo| zhd| ygh| psj| ntt| rlw| cmx| ukh| dzt| orm| xob| jtr| fyg| fxt| dtx| bom| pen| rfr| lvh| flu| tuh| ryd| hbk| uld| mvc| itp| cll| uqb| nvk| fpm| qgj| epa|