报告人：沈立新教授(美国雪城大学)

报告时间：2025年3月21日9:00-10:30

报告地点：腾讯会议598-559-724

报告摘要: This presentation focused on computing proximity operators for scale and signed permutation invariant functions. A scale-invariant function remains unchanged under uniform scaling, while a signed permutation invariant function retains its structure despite permutations and sign changes applied to its input variables. Noteworthy examples include the function and the ratios of $\ell_1/\ell_2$ and its square, with their proximity operators being particularly crucial in sparse signal recovery. We delve into the properties of scale and signed permutation invariant functions, delineating the computation of their proximity operators into three sequential steps: the $\vw$-step, $r$-step, and $d$-step. These steps collectively form a procedure termed as WRD, with the $\vw$-step being of utmost importance and requiring careful treatment. Leveraging this procedure, we present a method for explicitly computing the proximity operator of $(\ell_1/\ell_2)^2$ and introduce an efficient algorithm for the proximity operator of $\ell_1/\ell_2$.

 This presentation is accessible to senior undergraduate and graduate students.

 报告人简介：沈立新教授，现为美国雪城大学(Syracuse University)数学系、电气工程和计算机科学系终身教授。他于1987年本科毕业于北京大学，1990年在北京大学取得硕士学位，1996年在中山大学获数学博士学位。博士毕业后曾在新加坡国立大学、美国西密西根大学等工作，后于2006年加盟美国雪城大学数学系。其研究兴趣包括图像处理、最优化算法、计算调和分析等。已在国际知名期刊如：Appl. Comput. Harmon. Anal.，Inverse Problems, IEEE Trans. Image Process., IEEE Trans. Signal Process., SIAM J. Imaging Sci.等发表100余篇论文，并拥有多项美国发明专利。曾任Advan. Compt. Math 等杂志副主编。

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