主 講 人：韓德仁
講座時間：2020年12月3日19:30-20:30
講座地點：騰訊會議（會議號： 664 558 659； 密碼： 1203）
講座題目：Approximate first-order primal-dual algorithms for the saddle point problems
講座內(nèi)容：We introduce two approximate versions of the first-order primal-dual algorithm (PDA) for solving a class of convex-concave saddle point problems. The introduced approximate criteria are easy to implement in the sense that they only involve the subgradient of a certain function at the current iterate. The first approximate PDA solves both subproblems inexactly and adopts absolute error criteria, which are based on nonnegative summable sequences. The second approximate PDA, assuming that one of the PDA subproblems can be solved exactly, solves the other subproblem approximately and adopts a relative error criterion. The relative error criterion only involves a single parameter ranging in [0,1), which makes the method more applicable. For both versions, we establish the global convergence and O(1/N) rate of convergence measured by the iteration complexity, where N counts the number of iteration. Under further assumptions that partial of the underlying functions and the whole underlying functions are strongly convex, we show the accelerated O(1/N 2 ) and linear rate of convergence, respectively, for the inexact PDA with absolute error criteria. We then prove that these inexact criteria can also be extended to solve a class of more general problems. Finally, we perform some numerical experiments on sparse recovery and image processing problems, and the results demonstrate the feasibility and superiority of the proposed methods.
主講人簡介：韓德仁，教授、博士生導(dǎo)師，現(xiàn)任北京航空航天大學(xué)數(shù)學(xué)科學(xué)學(xué)院院長、教育部數(shù)學(xué)類專業(yè)教指委秘書長。2002年獲南京大學(xué)計算數(shù)學(xué)博士學(xué)位。從事大規(guī)模優(yōu)化問題、變分不等式問題的數(shù)值方法的研究工作，以及優(yōu)化和變分不等式問題在交通規(guī)劃、磁共振成像中的應(yīng)用，發(fā)表多篇學(xué)術(shù)論文。曾獲中國運籌學(xué)會青年運籌學(xué)獎，江蘇省科技進步二等獎等獎項。 主持國家自然科學(xué)基金杰出青年基金等多項項目，入選江蘇省333高層次人才培養(yǎng)工程。擔(dān)任中國運籌學(xué)會常務(wù)理事；《計算數(shù)學(xué)》、《Journal of the Operations Research Society of China》編委。
主辦：kaiyun開云官方網(wǎng)站信息與計算科學(xué)系
