Southwest Jiaotong University School of Mathematics


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西南交通大学理财网系列学术讲座:Approximate first-order primal-dual algorithms for the saddle point problems

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讲座地点:腾讯会议(会议号: 664 558 659 密码: 1203

讲座题目:Approximate first-order primal-dual algorithms for the saddle point problems

讲座内容: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.

主讲人简介:韩德仁,教授、博士生导师,现任北京航空航天大学数学科学学院院长、教育部数学类专业教指委秘书长。2002年获南京大学计算数学博士学位。从事大规模优化问题、变分不等式问题的数值方法的研究工作,以及优化和变分不等式问题在交通规划、磁共振成像中的应用,发表多篇学术论文。曾获中国运筹学会青年运筹学奖,江苏省科技进步二等奖等奖项。 主持国家自然科学基金杰出青年基金等多项项目,入选江苏省333高层次人才培养工程。担任中国运筹学会常务理事;《计算数学》、《Journal of the Operations Research Society of China》编委。