北京航空航天大学数学与系统科学学院应用数学导师介绍：夏勇

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导师详细信息

姓名：夏勇

性别：男

出生年份：1980

职称：副教授

院系：数学与系统科学学院

首次聘任导师时间：2013

现聘任导师一级学科名称：数学

现聘任导师二级学科名称：应用数学

聘任在第二学科培养博士生专业名称：无

聘任在自主设置学科培养博士生专业名称：无

主要研究方向及特色：运筹与优化

电子信箱：dearyxia@gmail.com

办公电话：82317930

办公地点：北京航空航天大学图书馆西配楼503

通信地址：北京航空航天大学数学与系统科学学院

个人简介：

1.个人情况简介

夏勇，男，(1980-)，2002年毕业于北京大学数学科学学院计算数学系，获理学学士学位和中国经济研究中心经济学双学士学位，2007年毕业于中国科学院数学与系统科学研究院，获理学博士学位（导师为袁亚湘院士）。2007年入职北京航空航天大学理学院数学系（现为：数学与系统科学学院）任讲师，2011年晋升副教授，2013年遴选为博士生导师。入选北航蓝天新星、北京市青年英才计划。曾任香港理工大学应用数学系研究助理、香港中文大学系统工程与工程管理系访问学者、台湾成功大学数学系客座助理教授。现任数学与系统科学学院统计、运筹与控制系系主任；中国运筹学会数学规划分会第六届理事；美国《数学评论》评论员。研究方向是运筹与优化：理论、模型与算法。

2.教学及人才培养情况，科研项目情况

教学：

本科生《概率统计》、《最优化理论与算法》、《数学软件》

研究生《现代优化方法》、《数学实验》、《数值分析》

出版教材：刘红英，夏勇，周水生《数学规划基础》，北京航空航天大学出版社，2012（2013获第三届中国大学出版社图书优秀奖(优秀教材一等奖),2013年北京高等教育精品教材）

指导研究生：毕业2名硕士(其中1人获校级优秀毕业论文)，在读硕士4人，博士1人。

参加北航2013“教书育人优秀研究生导师”评选获“最佳新锐奖”

科研项目：

[1]主持2010-2011唯实青年教师基金项目（编号：YWF-10-02-021）

[2]主持2011-2013国家自然科学基金青年基金项目“非凸二次优化的一些理论与应用”（编号：11001006）

[3]主持2011-2012软件开发环境国家重点实验室项目（编号：SKLSDE-2011ZX-15）

[4]主持2013-2014软件开发环境国家重点实验室项目（编号：SKLSDE-2013ZX-13）

[5]参加2012-2014国家自然科学基金培育项目“飞行器高雷诺数气动优化及动边界问题高精度快速算法研究”（编号：91130019/A011702）

[6]参加2015-2018国家自然科学基金“矩阵分解问题的优化算法和理论”（编号：11471325）

3.发表学术论文及科研成果

代表性的科研成果：

[1]二次指派问题方面的模型被国际顶级期刊《Operations Research》上的文章《Three Ideas for the Quadratic Assignment Problem》(作者Fischetti,Monaci和Salvagnin)用来求解了一类大规模问题，该文8次引用我们的模型，并称其为 Xia-Yuan model.被顶级期刊《INFORMS Journal on Computing》上的文章《The Robust (Minmax Regret) Quadratic Assignment Problem with Interval Flows》(作者Feizollahi 和 Averbakh) 一文11次引用，称其为Xia-Yuan linearization.

[2]独立获得了正交相似集凸包络的完美刻画。06年Ding和Wolkowicz 在一手稿中研究了矩阵的正交相似集的凸包络，给出了一些等价刻画，但是这些等价集合要么是无穷多个线性约束要么是非线性非凸约束，因而只能近似计算。我们巧妙构造性证明了正交相似集的凸包络可以由有限个线性矩阵不等式(LMI) 等价完整刻画! Ding 和Wolkowicz的论文在09年《Mathematics of Operations Research》正式发表时用一个评论谈及该项工作称``We failed to recognize this point in our initial work''

[3]回答了Zhu于2003年在《Journal of Optimzation Theory and Application》上提出的关于0-1与连续二次规划关联的一个公开问题。

[4]回答了Pinar和Teboulle于2006年在《RAIRO Operations Research》上提出的关于L1范数约束非凸二次规划的两个公开问题。

[5]Hiriart-Urruty于2007在《SIAM Review》提出了14个公开问题。其中第11个公开问题是问两个二次正定型乘积的Legendre-Fenchel conjugate，在假定函数是凸的前提下，Zhao于2010年在《SIAM Journal of Matrix Analysis & Applications》上回答了该问题。我们最近在不需要任何假定的前提下彻底回答了该公开问题。

[6]原创性地提出参数Lagrangian对偶方法，目前在0-1二次规划问题和界约束二次规划问题上有成功的应用。

[7]完美解决了等式约束S-lemma这一非凸二次优化领域的基础理论，论文被顶级期刊 《Mathematical Programming》录用。

[8]解决了Pong和Wolkowicz 在2014《Computational Optimization and Applications》关于双边广义信赖域子问题的强对偶成立充分条件的一个公开问题。至此，该问题的强对偶理论得以完全解决。

发表学术论文：

[1] Yong Xia and Ya-xiang Yuan, A New Linearization Method for Quadratic Assignment Problems,Optimization Methods & Software, 21(5): 803-816, 2006 (SCI )

[2] Yong Xia, A New Continuation Approach to Quadratic Assignment and Related Problems, In Ya-Xiang Yuan et al (Eds) Proceedings of the Eighth National Conference of Operations Research Society of China,Global-Link Informatics Limited, HongKong，2006: 262-269.

[3] Yong Xia, Improved Gilmore-Lawler bounds for quadratic assignment problems, Chinese Journal of Engineering Mathematics, vol. 24(3): 401-413, 2007

[4] Wajeb Gharibi, Yong Xia, A Dual Approach for Solving Nonlinear Infinity-Norm Minimization Problems with Applications in Separable Cases, Numer. Math. J. Chinese Univ. (English Ser.) issue 3, vol. 16: 265-270, 2007

[5] Yong Xia, Second Order Cone Programming Relaxation for the Quadratic Assignment Problem, Optimization Methods & Software, 23:3, 441-449, 2008 (SCI , EI)

[6] Yong Xia, Gilmore-Lawer bound of Quadratic Assignment Problem, Frontiers of Mathematics in China, 3(1): 109-118, 2008 (SCI )

[7] Yong Xia, Hongying Liu, Improving Upper Bound on the Capacity of Planar Wireless Networks with Omnidirectional Antennas, In Baozong Yuan and Xiaofang Tang (Eds) Proceedings of the IET 2nd International Conference on Wireless, Mobile & Multimedia Networks, 191-194, 2008 ( EI )

[8] Yong Xia, Wajeb Gharibi, A Study on the Quadratic Assignment Problem with Symmetric Rank-1 Input Matrices, Umm Al-Qura University Journal for Applied Sciences, Vol.1, No. 1, pp. 58-67, 2009

[9] Yong Xia, New Optimality Conditions for Quadratic Optimization Problems with Binary Constraints, Optimization Letters, vol.3(2): 253-263, 2009 (SCI )

[10] Yong Xia, Convex Hull Presentation of a Quadratically Constrained Set and its Application in Solving Quadratic Programming Problems, Asia-Pacific Journal of Operational Research, Vol.26, No.6, 769-778, 2009 (SCI )

[11] Yong Xia, New Sufficient Global Optimality Conditions for Linearly Constrained Bivalent Quadratic Optimization Problem, Journal of Industrial and Management Optimization,vol.5(4):881–892,2009 (SCI )

[12] Yong Xia and Hongying Liu, On The Interpoint Distance Sum Inequality,Journal of inequalities in pure and applied mathematics, Volume 10 (2009), Issue 3, Article 74, 10 pp.

[13] Yong Xia, An Efficient Continuation Method for Quadratic Assignment Problems,Computers & Operations Research,37:1027-1032, 2010 (SCI, EI )

[14] Wajeb Gharibi and Yong Xia, New Heuristic Rounding Approaches to the Quadratic Assignment Problem, Journal of Communication and Computer, Volume 7, No.4 (Serial No.65), 2010.

[15] 王艳萍，夏勇，Tammes问题的半正定规划松弛,中国运筹学会第十届学术交流会论文集, 117-123, 2010

[16] Yong Xia and Zi Xu, An Efficient Lagrangian Smoothing Heuristic for Max-Cut,Indian Journal of Pure and Applied Mathematics, 41(5): 683-700, 2010 (SCI )

[17] Hao Wang, Hongying Liu and Yong Xia,Two-step version of fixed point continuation method for sparse reconstruction, Front. Math. China 5(3), 575-588, 2010 (SCI )

[18] Xiaojin Zheng, Xiaoling Sun, Duan Li, Yong Xia, Duality Gap Estimation of Linear Equality Constrained Binary Quadratic Programming, MATHEMATICS OF OPERATIONS RESEARCH, 35(4), 864–880, 2010 (SCI)

[19] Yong Xia, Global Optimization of a Class of Nonconvex Quadratically Constrained Quadratic Programming Problems,Acta Mathematica Sinica, English Series,No.27(9),1803–1812 2011 (SCI )

[20] Hao Wang, Hongying Liu and Yong Xia,Two-point step-size iterative soft-thresholding method for sparse reconstruction, International Journal of Computer Mathematics, 88(12),2527-2537，2011 (SCI )

[21] Yong Xia, Xiaoling Sun, Duan Li,Xiaojin Zheng, On the Reduction of Duality Gap in Box Constrained Nonconvex Quadratic Program, SIAM journal on optimization, 21(3)，706-729，2011 (SCI)

[22] Yong Xia,Ruey-Lin Sheu, Xiaoling Sun, Duan Li,Improved Estimation of Duality Gap in Binary Quadratic Programming Using a Weighted Distance Measure, European Journal of Operational Research, 218(2): 351-357, 2012 (SCI )

[23] Joe-Mei Feng, Gang-Xuan Lin, Reuy-Lin Sheu and Yong Xia, Duality and Solutions for Quadratic Programming over Single Non-Homogeneous Quadratic Constraint,Journal of Global Optimization, (2012) 54(2):275–293 (SCI)

[24] Wajeb Gharibi, Yong Xia, A Tight Linearization Strategy for Zero-One Quadratic Programming Problems, International Journal of Computer Science Issues, (IJCSI) Volume 9, Issue 3(1), 294-299， 2012

[25]Yong Hsia and Yanping Wang, A New Penalty Parameter for Linearly Constrained 0-1 Quadratic Programming Problems, Optimization Letters， 7(4): 765-778, 2013 (SCI )

[26] Yong Xia, New semidefinite programming relaxations for box constrained quadratic program, SCIENCE CHINA Mathematics 56: 877–886 2013 (SCI)

[27] Yong Xia, Reuy-Lin Sheu,Xiaoling Sun, Duan Li, Tightening a Copositive Relaxation for Standard Quadratic Optimization Problems, Computational Optimization and Applications, 55:379–398, 2013 (SCI)

[28] Yong Xia, Convex Hull of the Orthogonal Similarity Set with Applications in Quadratic Assignment Problems, Journal of Industrial and Management Optimization, 9(3), 689-701, 2013 (SCI)

[29] Yong Xia, New Results on Semidefinite Bonds for L1-Constrained Nonconvex Quadratic Optimization, RAIRO Operations Research, 47(3): 285–297 2013 (SCI )

[30]韩颖薇 夏勇, 求解位姿估计问题的对偶方法, 运筹学学报, 17(3), 86-92, 2013

[31]曹文涛，夏勇, Kantorovich不等式的推广及其在最速下降法分析中的应用, 运筹与模糊学, 2013, 3, 35-39

[32] Yong Xia, A note on Legendre-Fenchel conjugate of the product of two positive-definite quadratic forms, Journal of Operations Research Society of China,1:333–338, 2013

[33] Yong Hsia, Baiyi Wu, Duan Li, New Reformulations for Probabilistically Constrained Quadratic Programs, European Journal of Operational Research, 233(3): 550–556, 2014 (SCI)

[34] Yong Hsia, Complexity and Nonlinear Semidefinite Programming Reformulation of L1-constrained Nonconvex Quadratic Optimization， Optimization Letters, 2014, 8:1433–1442 (SCI）

[35] Yong Xia, Yingwei Han，Partial Lagrangian Relaxation for the Unbalanced Orthogonal Procrustes Problem, Mathematical Methods of Operations Research, 79(2):225–237, 2014 (SCI)

[36] Yong Hsia,Gang-Xuan Lin, Reuy-Lin Sheu,A Revisit to Quadratic Programming with One Inequality Quadratic Constraint via Matrix Pencil, Pacific Journal of Optimization, 10(3): 461-481, 2014 (SCI)

[37]Yong Xia, On Local Convexity of Quadratic Transformations, Journal of Operations Research Society of China, 2(3):341-350, 2014

[38] Yong Xia, Wajeb Gharib, On Improving Convex Quadratic Programming Relaxation for the Quadratic Assignment Problem， Journal of Combinatorial Optimization, 2013, DOI 10.1007/s10878-013-9655-3 (SCI)

[39] Yong Xia, On Minimizing the Ratio of Quadratic Functions over an Ellipsoid， Optimization, 64(5), 1097–1106, 2015 (SCI)

[40] Yong Xia, Wenxun Xing, Parametric Lagrangian Dual for the Binary Quadratic Programming Problem, Journal of Global Optimization, 61:221–233, 2015 (SCI)

[41] Yu-Jun Gong, Yong Xia, On Sufficient Global Optimality Conditions for Bivalent Quadratic Programs with Quadratic Constraints, Asia-Pacific Journal of Operational Research, accepted 2014 (SCI)

[42]Shu Wang, Yong Xia, Strong Duality for Generalized Trust Region Subproblem: S-Lemma with Interval Bounds，Optimization Letters， accepted 2014 (SCI)

[43]Yong Xia, Ruey-Lin Sheu, Shu-Cherng Fang, Wenxun Xing, Double well potential function and its optimization in the n-dimensional real space: part II, Mathematics and Mechanics of Solids, to appear, 2015 (SCI)

[44]V.B. Nguyen, Ruey-Lin Sheu, Yong Xia, An SDP approach for quadratic fractional problems with a two-sided quadratic constraint. Optimization Methods & Software, DOI:10.1080/10556788.2015.1029575, 2015 (SCI)

[45]Yong Xia, Yu-Jun Gong and Sheng-Nan Han, A new semidefinite relaxation for L1-constrained quadratic optimization and extensions, Numerical Algebra, Control and Optimization, accepted 2015

[46]Yong Xia, Shu Wang, Ruey-Lin Sheu, S-Lemma with Equality and Its Applications, Mathematical Programming, DOI: 10.1007/s10107-015-0907-0, 2015 (SCI)

[47]Yong Hsia, Shu Wang,Zi Xu,Improved Semidefinite Approximation Bounds for Nonconvex Nonhomogeneous Quadratic Optimization with Ellipsoid Constraints, Operations Research Letters, accepted, 2015 (SCI)