本文選題：加速算法 + bundle��； 參考：《中國科學(xué):數(shù)學(xué)》2017年10期

【摘要】：本文提出了四種加速的BL(bundle level)算法來分別求解凸光滑函數(shù)、強(qiáng)凸光滑函數(shù)的極小值問題和一類鞍點(diǎn)(saddle-point)問題.這些算法可以運(yùn)用目標(biāo)函數(shù)的近似的一階信息來得到上述幾類問題的近似解.本文重點(diǎn)研究了在一階信息誤差上界可自由選取和給定不變的兩種情形下,所提出的算法中近似解能達(dá)到的最佳精度以及相應(yīng)的迭代復(fù)雜度.
[Abstract]:In this paper, we propose four accelerated BL(bundle level algorithms for solving convex smooth functions, strongly convex smooth functions and saddle-point saddle-point problems, respectively. These algorithms can use the first order information of the objective function to obtain the approximate solutions of the above problems. In this paper, we focus on the optimal accuracy of the approximate solution and the corresponding iterative complexity in the case that the upper bound of the first-order information error can be freely selected and given invariant.
【作者單位】： Department
【基金】：美國國家科學(xué)基金(批準(zhǔn)號(hào):DMS-1319050和DMS-1719932)資助項(xiàng)目
【分類號(hào)】：O174.13
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本文編號(hào)：1785979