变分分析与优化前沿论坛

变分分析与优化前沿论坛于2022年7月5日—7日在西南大学联合中国运筹学会举办。邀请变分分析与优化相关领域著名专家作学术报告。论坛宗旨展示与交流近年来变分分析与优化及其相关领域中的研究进展与取得的最新研究成果，研讨相关的前沿课题和近期的发展趋势，促进本学科的繁荣与发展；为本领域的科研与教学人员，特别是中青年，搭建相互交流与学习的平台。本届优化论坛是在由国家自然科学基金数学天元基金与西南大学资助的现代变分分析与数学优化专题讲习班结束时举办，参加专题讲习班的学员将有机会了解国内外在变分分析与优化及其相关领域中的研究进展与取得的最新研究成果。

邀请报告人(拼音字母序)：

边伟 (哈尔滨工业大学)

蔡邢菊(南京师范大学)

陈彩华 (南京大学)

陈志平 (西安交通大学)

郭磊 (华东理工大学)

韩德仁 (北京航空航天大学)

孟开文 (西南财经大学)

黄南京(四川大学)

黄正海（天津大学）

孔令臣（北京通交大学）

刘歆 (中国科学院数学与系统科学研究院)

刘新为(河北工业大学)

刘亚锋 (中国科学院数学与系统科学研究院)

凌晨(杭州电子科技大学)

孟志青 (浙江工业大学)

杨俊锋 (南京大学)

组织委员会：易尊尧、刘贤宁、王建军，陈加伟(召集人)

主办及资助单位：

国家自然科学基金、西南大学数学与统计学院

时间：2022年7月5日-7日

地点：西南大学与腾讯会议

联系人：陈加伟 电话：15123233235 邮箱：workshop2022swu@163.com

会议日程

报告题目及摘要

1、韩德仁 (北京航空航天大学)

Title:绝对值方程组和绝对值优化问题的分裂算法

Abstract：绝对值方程组问题和绝对值优化问题在信息领域，尤其是EDA领域有重要应用。本报告介绍求解绝对值方程组和绝对值优化问题的一些新进展，主要介绍一些分裂算法和对不相容问题的处理方法.

简介：韩德仁，北京航空航天大学教授，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，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、重点项目等多项项目。担任中国运筹学会常务理事、江苏省运筹学会理事长；《数值计算与计算机应用》《Journal of the Operations Research Society of China》《Journal of Global Optimization》编委。

2、刘歆 (中国科学院数学与系统科学研究院)

Title:Decentralizedoptimizationover thestiefelmanifold by anapproximateaugmented Lagrangianfunction

Abstract：We study the decentralized optimization problem over the Stiefel manifold, which is defined on a connected network of d agents. The objective is an average of d local functions, and each function is privately held by an agent and encodes its data. The agents can only communicate with their neighbors in a collaborative effort to solve this problem. In existing methods, multiple rounds of communications are required to guarantee the convergence, giving rise to high communication costs. In contrast, this paper proposes a decentralized algorithm, called DESTINY, which only invokes a single round of communications per iteration. DESTINY combines gradient tracking techniques with a novel approximate augmented Lagrangian function. The global convergence to stationary points is rigorously established. Comprehensive numerical experiments demonstrate that DESTINY has a strong potential to deliver a cutting-edge performance in solving a variety of testing problems.

简介：刘歆，中国科学院数学与系统科学研究院，冯康首席研究员。2004年本科毕业于北京大学数学科学学院；2009年于中国科学院数学与系统科学研究院获得博士学位；毕业后留所工作至今。曾在德国Zuse Institute Berlin，美国Rice大学，美国纽约大学Courant研究所等科研院所长期访问。主要研究方向包括：流形优化、分布式优化、统计大数据分析、材料计算、机器学习等。2016年获得国家优秀青年科学基金；2016年获得中国运筹学会青年科技奖；2020年获得中国工业与应用数学学会应用数学青年科技奖；2021年获得国家杰出青年科学基金。目前担任《Mathematical Programming Computation》、《Journal of Computational Mathematics》、《Journal of Industrial and Management Optimization》等期刊编委；担任中国运筹学会常务理事，中国工业与应用数学会副秘书长。

3、黄南京 (四川大学)

Title:两类分数阶微分半变分不等式及其应用

Abstract：在本报告中，我们考虑了一类分数阶微分拟半变分不等式问题,获得了解的存在性和唯一性结果; 研究了函数扰动意义下该类问题解的稳定性问题,获得了稳定性刻画结果。同时，我们考虑了一类分数阶微分发展性半变分不等式问题, 获得了解的存在性和唯一性结果; 研究了逼近问题解的全离散格式,给出相应的数值分析结果。 作为应用， 我们把上述研究所得理论结果用于研究接触力学中的相关问题。

简介：黄南京，博士，四川大学二级教授，运筹学和控制论以及金融数学专业博士生导师，四川省学术带头人，四川省专家评议（审）委员会成员，中国运筹学会常务理事。主要研究方向为优化理论及应用、非线性分析及应用、金融数学、优化与物流管理等。主持国家自然科学基金和教育部基金项目多项，在变分不等式和互补问题理论及应用、不动点理论及应用、向量优化和均衡问题的理论及其应用、金融资产定价和投资组合优化等方面的研究工作得到了国内外同行的好评，解决了加拿大、匈牙利和国内知名学者提出的关于优化方面的3个公开问题，连续5年（2014-2019）入选Elsevier中国高引文学者。

4、孟开文 (西南财经大学)

Title: Lipschitz-like property relative to a set and the generalized Mordukhovich criterion

Abstract：In this paper we will establish some necessary condition and sufficient condition respectively for a set-valued mapping to have the Lipschitz-like property relative to a closed set by employing regular normal cone and limiting normal cone of a restricted graph of the set-valued mapping. We will obtain a complete characterization for a set-valued mapping to have the Lipschitz-property relative to a closed and convex set by virtue of the projection of the coderivative onto a tangent cone. Furthermore, by introducing a projectional coderivative of set-valued mappings, we establish a verifiable generalized Mordukhovich criterion for the Lipschitz-like property relative to a closed and convex set. We will study the representation of the graphical modulus of a set-valued mapping relative to a closed and convex set by using the outer norm of the corresponding projectional coderivative value. For an extended real-valued function, we will apply the obtained results to investigate itsrelativeLipschitz continuity and the Lipschitz-like property of a level-set mapping relative to a half line.

简介：孟开文，香港理工大学博士，西南财经大学数学学院副教授，博士生导师。主要从事最优化理论、算法和应用研究，主持国家自然科学基金青年和面上项目各一项。在Operations Research，Mathematical Programming，Journal of Machine Learning Research，SIAM Journal on Optimization，Journal of Convex Analysis等期刊上发表学术论文十余篇。

5、边伟 (哈尔滨工业大学)

Title:Exact continuous relaxations and algorithms for

regularized optimization problems

Abstract：In this talk, we considertwo classes of

regularized optimization problems, in which the group sparsity is considered.Firstly, we givethe continuous relaxation models of the considered problem and establish the equivalence of these two problems in the sense of global minimizers. Then, we define a class of stationary points of the relaxation problem, and prove that any defined stationary point is a local minimizer of the considered

regularized problem and satisfies a desirable property of its global minimizers. Further, based on the difference-of-convex (DC) structure of the relaxation problem, we designsome corresponding algorithms and provetheir convergence properties. Finally, some numerical experimentsare illustratedto show the efficiency of the proposed algorithms.

简介：边伟，哈尔滨工业大学数学学院，教授、博士生导师。2004年和2009年于哈尔滨工业大学分别获得学士和博士学位，随后入职哈工大数学学院。2010-2012年访问香港理工大学跟随陈小君教授，从事博士后工作。主要从事的研究领域为：最优化理论与算法、神经网络。先后在 MP, SIOPT, SIIMS, SINUA，SISC,MOR和四个IEEE系列汇刊发表多篇学术论文。先后主持3项国家自然科学基金项目，并获得2018年度 “龙江青年学者”和2019年度国家级青年人才。现任中国运筹学会理事，中国运筹学会数学规划分会理事，黑龙江数学会常务理事，国际期刊JOTA编委。

6、郭磊 (华东理工大学)

Title: A New Augmented Lagrangian Method for MPCCs - Theoretical and Numerical Comparison with Existing Augmented Lagrangian Methods

Abstract：We propose a new augmented Lagrangian (AL) method for solving the mathematical program with complementarity constraints (MPCC), where the complementarity constraints are left out of the AL function and treated directly. Two observations motivate us to propose this method: the AL subproblems are closer to the original problem in terms of the constraint structure; and the AL subproblems can be solved efficiently by a nonmonotone projected gradient method, in which we have closed-form solutions at each iteration. The former property helps us show that the proposed method converges globally to an M-stationary (better than C-stationary) point under MPCC relaxed constant positive linear dependence condition. Theoretical comparison with existing AL methods demonstrates that the proposed method is superior in terms of the quality of accumulation points and the strength of assumptions. Numerical comparison, based on problems in MacMPEC, validates the theoretical results.

简介：郭磊，博士生导师，2013年博士毕业于大连理工大学，师从林贵华教授，2019年至今工作于华东理工大学。曾先后在上海交通大学、加拿大维多利亚大学、香港浸会大学等工作与合作研究。曾获得辽宁省优秀博士学位论文、教育部首届博士研究生国家奖学金等，主要从事最优化理论及应用研究，主持国家自然科学基金项目等多项，在Mathematical Programing、SIAM Journal on Optimization等重要期刊发表论文10余篇。

7、蔡邢菊(南京师范大学)

Title:An balanced Douglas-Rachford splitting algorithm for convex minimization

Abstract：The Douglas-Rachford algorithm is a classical and effective splitting method to solve the inclusion problems. Recently, an adaptive Douglas-Rachford splitting algorithm is proposed for the monotone inclusion, which allow one operator be weakly monotone. We apply the idea of adaptive Douglas-Rachford splitting method (ADRSM) to differentiable convex optimization problems with abstract constraints, and more attractive results can be obtained for the convex optimization problem. We propose accurate and inaccurate versions of the algorithm respectively, and prove the global convergence of the algorithms. We extend these results to two separable convex optimization problems with linear constraints. In numerical experiments, we compare our algorithms with other commonly used algorithms and the results verify the effectiveness of our algorithms.

简介：蔡邢菊，南京师范大学教授。主要从事最优化理论与算法、变分不等式、数值优化方向。发表SCI论文三十余篇。主持国家青年基金、面上基金、省青年基金各一项，参加国家重点项目一项，获江苏省科技进步奖一等奖一项。担任中国运筹学会副秘书长、江苏省运筹学会秘书长。

8、陈彩华 (南京大学)

Title:Algorithmic Design for Wasserstein Distributionally Learning

Abstract：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.

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。

窗体底端

9、黄正海 (天津大学)

Title:Tensor Robust Principal Component Analysis via Tensor Fibered Rank and LP Minimization

Abstract：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.

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。

10、凌晨 (杭州电子科技大学)

Title:Tensor Completion via A Generalized Transformed Tensor T-Product Decomposition without t-SVD

Abstract：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.

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。

11、刘新为 (河北工业大学)

Title:A new augmented Lagrangian method for inequality constrained optimization

Abstract：We introduce a twice differentiable augmented Lagrangian and present a novel augmented Lagrangian method of multipliers for optimization with general inequality constraints. Our method is a combination of the augmented Lagrangian and the logarithmic-barrier technique, and is a generalization of the Hestenes-Powell augmented Lagrangian. Without assuming any constraint qualification, it is proved that our method has strong global convergence. Locally, our method is capable of rapidly detecting the possible infeasibility, and has linearly convergence to the KKT point. The preliminary numerical experiments on some small benchmark test problems demonstrate our theoretical results.

简介：刘新为教授，博导，1998年博士毕业于中国科学院计算数学与科学工程计算研究所，师从袁亚湘院士。现任河北工业大学数学研究院常务副院长，兼任河北工业大学校学术委员会委员、理学院学术委员会主任，中国运筹学会常务理事、中国运筹学会数学规划分会常务理事，中国数学会计算数学分会理事，河北省运筹学会副理事长兼秘书长，河北省数学会计算数学分会理事长，英文SCI刊物《Mathematical Methods of Operations Research》、《Pacific Journal of Optimization》和《计算数学》编委。先后主持5项国家自然科学基金面上项目、参与1项国家自然科学基金重大研究计划项目。主要研究非凸非线性优化算法及其收敛性理论，在《Mathematical Programming》、《SIAM Journal on Optimization》、《SIAM Journal on Scientific Computing》、《Mathematics of Computation》及《IEEE Transactions on Neural Networks and Learning Systems》等国际重要刊物发表多篇论文。

12、孟志青 (浙江工业大学)

Title:An Objective Penalty Function Method for Biconvex Programming

Abstract：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.

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。

13、陈志平 (西安交通大学)

Title:Distributionally robust stochastic dominance constrained optimization with Wasserstein distance

Abstract：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.

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。

14、孔令臣 (北京交通大学)

Title:Newton method for the composite row sparsity regularized optimization

Abstract：This paper is concerned with the composite row sparsity regularized (cRSR) minimization problem, which captures a number of important applications arising in machine learning, statistics, signal and image processing, and so forth. Due to the non-convexity and discontinuity of the composite row sparsity regularization term, the cRSR problem is NP-hard in general. In this paper, we study the optimality conditions of the cRSR problem and derive its stationary equation which is crucial to design efficient algorithm. Based on this stationary equation, an easy-to-implement Newton method is designed to solve the cRSR problem (NcRSR for short). The quadratic convergence rate and iteration complexity estimation of the NcRSR are rigorously proved under some mild conditions. To demonstrate the effectiveness of NcRSR, we apply it to solve the simultaneous clustering and optimization and trend filtering problems. Extensive experimental results illustrate that our approach has superior performance comparing to the state-of-the-art methods. In particular, NcRSR possesses not only perfect clustering performance and estimation accuracy but also one hundred times faster than the first-order methods.

简介：孔令臣博士，北京交通大学数学与统计学院，教授，博士生导师，中国运筹学会数学规划分会副秘书长。2007年毕业于北京交通大学，获博士学位。2007-2009年，加拿大滑铁卢大学组合与优化系博士后。2009年9月入职北京交通大学数学系，2010年晋升为副教授，2014年晋升为教授。主要从事统计优化、高维统计分析、稀疏优化、对称锥互补和优化问题以及医学和交通应用等方面的研究。主持国家自然科学基金面上项目和参与973课题、国家自然科学基金重点项目以及北京市自然科学基金重点项目等，获得2012度中国运筹学会青年奖。

15、刘亚锋 (中国科学院数学与系统科学研究院)

Title:Uplink-Downlink Duality in Wireless Communications: Where Lagrange Meets Shannon（从优化的视角看无线通信中的上下行对偶：一场拉格朗日和香农的对话）

Abstract：Many problems arising from communication system design can be formulated as optimization problems. In practice, one is often interested in not only the numerical solution to the problems but also the special structure of their optimal solution. In this talk, we shall use some examples from wireless communications and information theory to show that exploring the Lagrangian dual of these (convex) problems often reveal the structure of their optimal solution and the structure of the optimal solution will further lead to better algorithms for solving the corresponding problems.

简介：刘亚锋，2007年毕业于西安电子科技大学理学院数学系，2012年在中国科学院数学与系统科学研究院获得博士学位（导师：戴彧虹研究员）；博士期间，受中国科学院数学与系统科学研究院资助访问明尼苏达大学一年（合作导师：罗智泉院士）。博士毕业后，他一直在中国科学院数学与系统科学研究院计算数学所工作，2018年晋升为数学与系统科学研究院副研究员。他的主要研究兴趣是最优化理论与算法及其在信号处理和无线通信等领域中的应用。曾获2011年国际通信大会“最佳论文奖”，2018年数学与系统科学研究院“陈景润未来之星”，2018年中国运筹学会“青年科技奖”，2020年IEEE通信学会亚太地区“杰出青年学者奖”等。他目前担任《IEEE Transactions on Wireless Communications》、《IEEE Signal Processing Letters》和《Journal of Global Optimization》期刊的编委。他是IEEE信号处理学会SPCOM（Signal Processing for Communications and Networking）的技术委员会成员。他的工作获得国家自然科学基金委青年基金、面上项目和优秀青年基金的资助。

16、杨俊锋 (南京大学)

Title:Primal-Dual Splitting Methods Constructed Based on Convex Combination

Abstract：Recently, we have proposed using convex combination technique to construct new primal-dual full splitting algorithms for solving some structured convex optimization problems. In this talk, I will review the proposed algorithms and their convergence properties. A connection to the primal-dual algorithm of Chambolle and Pock will also be given. Recently, we have proposed a golden ratio primal dual algorithm (GRPDA) for solving structured convex optimization problems and it can be viewed as a new adaptation of the classical Arrow-Hurwicz method using a convex combination technique. The convex combination technique has been applied to several related problems.

简介：杨俊锋是南京大学数学系教授、博导。先后师从中国科学院袁亚湘院士、南京大学何炳生教授、美国莱斯大学张寅教授。主要从事最优化计算方法及其应用研究，在SIAM J Optim, Comput Optim Appl等权威期刊发表数十篇论文，开发图像去模糊软件包FTVd、压缩感知L1模解码软件包YALL1等。曾获国家优秀青年基金、中国运筹学会青年科技奖，入选教育部新世纪优秀人才支持计划。