北京航空航天大學數學與系統科學學院應用數學導師介紹：夏勇

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導師詳細信息

姓名：夏勇

性別：男

出生年份：1980

職稱：副教授

院系：數學與系統科學學院

首次聘任導師時間：2013

現聘任導師一級學科名稱：數學

現聘任導師二級學科名稱：應用數學

聘任在第二學科培養博士生專業名稱：無

聘任在自主設置學科培養博士生專業名稱：無

主要研究方向及特色：運籌與優化

電子信箱：dearyxia@gmail.com

辦公電話：82317930

辦公地點：北京航空航天大學圖書館西配樓503

通信地址：北京航空航天大學數學與系統科學學院

個人簡介：

1.個人情況簡介

夏勇，男，(1980-)，2002年畢業于北京大學數學科學學院計算數學系，獲理學學士學位和中國經濟研究中心經濟學雙學士學位，2007年畢業于中國科學院數學與系統科學研究院，獲理學博士學位（導師為袁亞湘院士）。2007年入職北京航空航天大學理學院數學系（現為：數學與系統科學學院）任講師，2011年晉升副教授，2013年遴選為博士生導師。入選北航藍天新星、北京市青年英才計劃。曾任香港理工大學應用數學系研究助理、香港中文大學系統工程與工程管理系訪問學者、臺灣成功大學數學系客座助理教授。現任數學與系統科學學院統計、運籌與控制系系主任；中國運籌學會數學規劃分會第六屆理事；美國《數學評論》評論員。研究方向是運籌與優化：理論、模型與算法。

2.教學及人才培養情況，科研項目情況

教學：

本科生《概率統計》、《最優化理論與算法》、《數學軟件》

研究生《現代優化方法》、《數學實驗》、《數值分析》

出版教材：劉紅英，夏勇，周水生《數學規劃基礎》，北京航空航天大學出版社，2012（2013獲第三屆中國大學出版社圖書優秀獎(優秀教材一等獎),2013年北京高等教育精品教材）

指導研究生：畢業2名碩士(其中1人獲校級優秀畢業論文)，在讀碩士4人，博士1人。

參加北航2013“教書育人優秀研究生導師”評選獲“最佳新銳獎”

科研項目：

[1]主持2010-2011唯實青年教師基金項目（編號：YWF-10-02-021）

[2]主持2011-2013國家自然科學基金青年基金項目“非凸二次優化的一些理論與應用”（編號：11001006）

[3]主持2011-2012軟件開發環境國家重點實驗室項目（編號：SKLSDE-2011ZX-15）

[4]主持2013-2014軟件開發環境國家重點實驗室項目（編號：SKLSDE-2013ZX-13）

[5]參加2012-2014國家自然科學基金培育項目“飛行器高雷諾數氣動優化及動邊界問題高精度快速算法研究”（編號：91130019/A011702）

[6]參加2015-2018國家自然科學基金“矩陣分解問題的優化算法和理論”（編號：11471325）

3.發表學術論文及科研成果

代表性的科研成果：

[1]二次指派問題方面的模型被國際頂級期刊《Operations Research》上的文章《Three Ideas for the Quadratic Assignment Problem》(作者Fischetti,Monaci和Salvagnin)用來求解了一類大規模問題，該文8次引用我們的模型，并稱其為 Xia-Yuan model.被頂級期刊《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，稱其為Xia-Yuan linearization.

[2]獨立獲得了正交相似集凸包絡的完美刻畫。06年Ding和Wolkowicz 在一手稿中研究了矩陣的正交相似集的凸包絡，給出了一些等價刻畫，但是這些等價集合要么是無窮多個線性約束要么是非線性非凸約束，因而只能近似計算。我們巧妙構造性證明了正交相似集的凸包絡可以由有限個線性矩陣不等式(LMI) 等價完整刻畫! Ding 和Wolkowicz的論文在09年《Mathematics of Operations Research》正式發表時用一個評論談及該項工作稱``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》上提出的關于0-1與連續二次規劃關聯的一個公開問題。

[4]回答了Pinar和Teboulle于2006年在《RAIRO Operations Research》上提出的關于L1范數約束非凸二次規劃的兩個公開問題。

[5]Hiriart-Urruty于2007在《SIAM Review》提出了14個公開問題。其中第11個公開問題是問兩個二次正定型乘積的Legendre-Fenchel conjugate，在假定函數是凸的前提下，Zhao于2010年在《SIAM Journal of Matrix Analysis & Applications》上回答了該問題。我們最近在不需要任何假定的前提下徹底回答了該公開問題。

[6]原創性地提出參數Lagrangian對偶方法，目前在0-1二次規劃問題和界約束二次規劃問題上有成功的應用。

[7]完美解決了等式約束S-lemma這一非凸二次優化領域的基礎理論，論文被頂級期刊 《Mathematical Programming》錄用。

[8]解決了Pong和Wolkowicz 在2014《Computational Optimization and Applications》關于雙邊廣義信賴域子問題的強對偶成立充分條件的一個公開問題。至此，該問題的強對偶理論得以完全解決。

發表學術論文：

[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] 王艷萍，夏勇，Tammes問題的半正定規劃松弛,中國運籌學會第十屆學術交流會論文集, 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]韓穎薇 夏勇, 求解位姿估計問題的對偶方法, 運籌學學報, 17(3), 86-92, 2013

[31]曹文濤，夏勇, Kantorovich不等式的推廣及其在最速下降法分析中的應用, 運籌與模糊學, 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)