变分分析与优化前沿论坛(7月6日上午)

学术报告（一）

报告题目：Distributionally robust stochastic dominance constrained optimization with Wasserstein distance

报告人：陈志平 (西安交通大学)

报告时间：2022年7月6日8:30-

腾讯会议：394-2491-2514 密码：123123

参加人员：本科生、研究生、教师

报告摘要：We consider a distributionally robust second-order stochastic dominance constrained optimization problem, where the true distribution of the uncertain parameters is ambiguous. The ambiguity set contains all probability distributions close to the empirical distribution under the Wasserstein distance. We adopt the sample approximation technique to develop a linear programming formulation that provides a lower bound. We propose a novel split-and-dual decomposition framework which provides an upper bound. We prove that both lower and upper bound approximations are asymptotically tight when there are enough samples or pieces. To efficiently solve the non-convex upper bound problem, we use a sequential convex approximation algorithm. Numerical evidences on a portfolio selection problem valid the efficiency and asymptotically tightness of the proposed two approximation methods.

报告人简介：陈志平西安交通大学数学与统计学院教授、博士生导师、英国剑桥大学博士后。长期从事随机规划理论及其应用、分布式鲁棒优化、金融风险度量与投资分析等领域的研究，在SIAM Journal on Optimization，Journal of Optimization Theory and Applications, European Journal of Operational Research，Journal of Banking＆Finance, Journal of Economic Dynamics and Control, Insurance: Mathematics and Economics等运筹学、经济与金融期刊发表SCI（SSCI）检索论文多篇。主持国家自然科学基金重大项目等多项。现为《OR Spectrum》编委，《Big Data and Information Analytics》编委、《工程数学学报》编委、编辑部主任；现任中国运筹学会金融工程与金融风险管理分会副会长、常务理事，中国管理科学与工程学会金融计量与风险管理研究会常务理事。担任西安交通大学西安数学与数学技术研究院常务副院长、国家天元数学西北中心副主任。

窗体底端

学术报告（二）

报告题目：Tensor Robust Principal Component Analysis via Tensor Fibered Rank and LP Minimization

报告人：黄正海 (天津大学)

报告时间：2022年7月6日9:10-

腾讯会议：394-2491-2514 密码：123123

参加人员：本科生、研究生、教师

报告摘要：Tensor Robust Principal Component Analysis (TRPCA) is an important method to handle high-dimensional data and has been widely used in many areas. In this paper, we mainly focus on the TRPCA problem based on tensor fibered rank for sparse noise removal, which aims to recover the low-fibered-rank tensor from grossly corrupted observations. Usually, the L1-norm is used as a convex approximation of tensor rank, but it is essentially biased and fails to achieve the best estimation performance. Therefore, we first propose a novel nonconvex model named as TRPCAp, in which the Lp penalty is adopted to approximate tensor fibered rank and measure sparsity. Then, an error bound of the estimator of TRPCA Lp is established and this error bound can be better than those of similar models based on Tucker rank or tubal rank. Further, we present an efficient algorithm based on alternating direction method of multipliers to solve TRPCAp and provide convergence guarantee for this algorithm. Finally, extensive experiments on color images, videos and hyperspectral images demonstrate the effectiveness of the proposed method.

报告人简介：黄正海，天津大学数学学院教授、博士生导师。主要从事最优化理论、算法及其应用方面的研究工作，在求解互补与变分不等式问题、对称锥优化与对称锥互补问题、稀疏优化、张量优化、核磁共振医学成像、人脸识别等方面取得了一些有意义的成果。目前的主要研究兴趣是张量优化、特殊结构的变分不等式与互补问题、以及机器学习中的优化理论方法及其应用。已发表SCI检索论文120多篇、连续获得多项国家自然科学基金资助。曾获得中科院优秀博士后奖和教育部高等学校自然科学奖二等奖。目前为中国运筹学会常务理事；《Pacific Journal of Optimization》、《Applied Mathematics and Computation》、《Optimization,Statistics & Information Computing》和《运筹学学报》的编委。

学术报告（三）

报告题目：Tensor Completion via A Generalized Transformed Tensor T-Product Decomposition without t-SVD

报告人：凌晨 (杭州电子科技大学)

报告时间：2022年7月6日9:50-

腾讯会议：394-2491-2514 密码：123123

参加人员：本科生、研究生、教师

报告摘要：Matrix and tensor nuclear norms have been successfully used to promote the low-rankness of tensors in low-rank tensor completion. However, singular value decomposition (SVD), which is computationally expensive for large-scale matrices, frequently appears in solving these nuclear norm minimization models. Based on the tensor-tensor product (T-product), in this talk, we first establish the equivalence between the so-called transformed tubal nuclear norm for a third order tensor and the minimum of the sum of two factor tensors’squared Frobenius norms under a general invertible linear transform. Gainfully, we introduce a spatio-temporal regularized tensor completion model that is able to maximally preserve the hidden structures of tensors. Then, we propose an implementable alternating minimization algorithm to solve the underlying optimization model. It is remarkable that our approach does not require any SVDs and all subproblems of our algorithm have closed-form solutions. A series of numerical experiments on traffic data recovery, color images and videos inpainting demonstrate that our SVD-free approach takes less computing time to achieve satisfactory accuracy than some state-of-the-art tensor nuclear norm minimization approaches. This is a joint work with H. J. He and W. H. Xie。

报告人简介：杭州电子科技大学理学院教授，博士生导师。现任中国运筹学会数学规划分会副理事长、中国经济数学与管理数学研究会副理事长，曾任中国运筹学会理事、中国系统工程学会理事、浙江省数学会常务理事。近十年来，主持国家自科基金和浙江省自科基金各4项、其中省基金重点项目1项。在国内外重要刊物发表论文80余篇，多篇发表在Math. Program.、SIAM J. on Optim.和 SIAM J.on Matrix Anal.and Appl. 、COAP、JOTA、JOGO等。

学术报告（四）

报告题目：An Objective Penalty Function Method for Biconvex Programming

报告人：孟志青 (浙江工业大学)

报告时间：2022年7月6日10:40-

腾讯会议：394-2491-2514 密码：123123

参加人员：本科生、研究生、教师

报告摘要：Biconvex programming is nonconvex optimization describing many practical problems. The existing research shows that the difficulty in solving biconvex programming makes it a very valuable subject to find new theories and solution methods. This paper first obtains two important theoretical results about partial optimum of biconvex programming by the objective penalty function. One result holds that the partial Karush-Kuhn-Tucker(KKT) condition is equivalent to the partially exactness for the objective penalty function of biconvex programming. Another result holds that the partial stability condition is equivalent to the partially exactness for the objective penalty function of biconvex programming. These results provide a guarantee for the convergence of algorithms for solving a partial optimum of biconvex programming. Then, based on the objective penalty function, three algorithms are presented for finding an approximate $\epsilon$-solution to partial optimum of biconvex programming, and their convergence is also proved. Finally, numerical experiments show that an $\epsilon$-feasible solution is obtained by the proposed algorithm.

报告人简介：孟志青，博士，浙江工业大学管理学院教授，浙江省优秀教师。中国运筹学学理事，决策科学学会常务理事、随机服务系统与运作管理分会常务理事和数学规划分会理事。杭州市第一批工业企业信息化专家。研究方向为最优化理论、风险管理、供应链管理、数据挖掘等，先后承担过国家自然科学基金、省自然科学基金和省哲学社会科学规划基金等项目，在国内外学术杂志上共发表学术论文150多篇，出版专著《凸分析与非光滑分析》、《目标罚函数算法》、《时态数据挖掘算法》、《多目标条件风险值理论》和《竞争与合作》等。

学术报告（五）

报告题目：Algorithmic Design for Wasserstein Distributionally Learning

报告人：陈彩华 (南京大学)

报告时间：2022年7月6日11:20-

腾讯会议：394-2491-2514 密码：123123

参加人员：本科生、研究生、教师

报告摘要：Wasserstein Distributionally Robust Stochastic Optimization (DRSO) is concerned with finding decisions that perform well on data that are drawn from the worst-case probability distribution within a Wasserstein ball centered at a certain nominal distribution. In recent years, it has been shown that various DRSO formulations of learning models admit tractable convex reformulations. However, most existing works propose to solve these convex reformulations by general-purpose solvers, which are not well-suited for tackling large-scale problems. In this talk, we focus on Wasserstein distributionally robust support vector machine (DRSVM) problems and logistic regression (DRLR) problems, and propose two novel first order algorithms to solve them. The updates in each iteration of these algorithms can be computed in a highly efficient manner. Our numerical results indicate that the proposed methods are orders of magnitude faster than the state-of-the-art, and the performance gap grows considerably as the problem size increases. Advanced models such as robust classification with fairness and unlabelled data are also discussed.

报告人简介：陈彩华，教授，博士生导师，南京大学工程管理学院副院长，新加坡国立大学联合培养博士，曾赴新加坡国立大学、香港中文大学等学习与访问。主持国家自然科学基金优秀青年项目、面上项目以及青年项目等3项，参与国家自然科学基金重点项目1项。在《Mathematical Programming》，《SIAM Journal on Optimization》等最优化顶级期刊发表学术论文多篇。2017和2018连续两年获华人数学家联盟最佳论文奖，2018年获中国运筹学会青年科技奖以及入选首批南京大学仲英青年学者，2019年获南京大学青年五四奖章，2019年获江苏省社科优青。