北京航空航天大學(xué)數(shù)學(xué)與系統(tǒng)科學(xué)學(xué)院應(yīng)用數(shù)學(xué)導(dǎo)師介紹：夏勇

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導(dǎo)師詳細(xì)信息

姓名：夏勇

性別：男

出生年份：1980

職稱：副教授

院系：數(shù)學(xué)與系統(tǒng)科學(xué)學(xué)院

首次聘任導(dǎo)師時(shí)間：2013

現(xiàn)聘任導(dǎo)師一級(jí)學(xué)科名稱：數(shù)學(xué)

現(xiàn)聘任導(dǎo)師二級(jí)學(xué)科名稱：應(yīng)用數(shù)學(xué)

聘任在第二學(xué)科培養(yǎng)博士生專業(yè)名稱：無

聘任在自主設(shè)置學(xué)科培養(yǎng)博士生專業(yè)名稱：無

主要研究方向及特色：運(yùn)籌與優(yōu)化

電子信箱：dearyxia@gmail.com

辦公電話：82317930

辦公地點(diǎn)：北京航空航天大學(xué)圖書館西配樓503

通信地址：北京航空航天大學(xué)數(shù)學(xué)與系統(tǒng)科學(xué)學(xué)院

個(gè)人簡介：

1.個(gè)人情況簡介

夏勇，男，(1980-)，2002年畢業(yè)于北京大學(xué)數(shù)學(xué)科學(xué)學(xué)院計(jì)算數(shù)學(xué)系，獲理學(xué)學(xué)士學(xué)位和中國經(jīng)濟(jì)研究中心經(jīng)濟(jì)學(xué)雙學(xué)士學(xué)位，2007年畢業(yè)于中國科學(xué)院數(shù)學(xué)與系統(tǒng)科學(xué)研究院，獲理學(xué)博士學(xué)位（導(dǎo)師為袁亞湘院士）。2007年入職北京航空航天大學(xué)理學(xué)院數(shù)學(xué)系（現(xiàn)為：數(shù)學(xué)與系統(tǒng)科學(xué)學(xué)院）任講師，2011年晉升副教授，2013年遴選為博士生導(dǎo)師。入選北航藍(lán)天新星、北京市青年英才計(jì)劃。曾任香港理工大學(xué)應(yīng)用數(shù)學(xué)系研究助理、香港中文大學(xué)系統(tǒng)工程與工程管理系訪問學(xué)者、臺(tái)灣成功大學(xué)數(shù)學(xué)系客座助理教授。現(xiàn)任數(shù)學(xué)與系統(tǒng)科學(xué)學(xué)院統(tǒng)計(jì)、運(yùn)籌與控制系系主任；中國運(yùn)籌學(xué)會(huì)數(shù)學(xué)規(guī)劃分會(huì)第六屆理事；美國《數(shù)學(xué)評(píng)論》評(píng)論員。研究方向是運(yùn)籌與優(yōu)化：理論、模型與算法。

2.教學(xué)及人才培養(yǎng)情況，科研項(xiàng)目情況

教學(xué)：

本科生《概率統(tǒng)計(jì)》、《最優(yōu)化理論與算法》、《數(shù)學(xué)軟件》

研究生《現(xiàn)代優(yōu)化方法》、《數(shù)學(xué)實(shí)驗(yàn)》、《數(shù)值分析》

出版教材：劉紅英，夏勇，周水生《數(shù)學(xué)規(guī)劃基礎(chǔ)》，北京航空航天大學(xué)出版社，2012（2013獲第三屆中國大學(xué)出版社圖書優(yōu)秀獎(jiǎng)(優(yōu)秀教材一等獎(jiǎng)),2013年北京高等教育精品教材）

指導(dǎo)研究生：畢業(yè)2名碩士(其中1人獲校級(jí)優(yōu)秀畢業(yè)論文)，在讀碩士4人，博士1人。

參加北航2013“教書育人優(yōu)秀研究生導(dǎo)師”評(píng)選獲“最佳新銳獎(jiǎng)”

科研項(xiàng)目：

[1]主持2010-2011唯實(shí)青年教師基金項(xiàng)目（編號(hào)：YWF-10-02-021）

[2]主持2011-2013國家自然科學(xué)基金青年基金項(xiàng)目“非凸二次優(yōu)化的一些理論與應(yīng)用”（編號(hào)：11001006）

[3]主持2011-2012軟件開發(fā)環(huán)境國家重點(diǎn)實(shí)驗(yàn)室項(xiàng)目（編號(hào)：SKLSDE-2011ZX-15）

[4]主持2013-2014軟件開發(fā)環(huán)境國家重點(diǎn)實(shí)驗(yàn)室項(xiàng)目（編號(hào)：SKLSDE-2013ZX-13）

[5]參加2012-2014國家自然科學(xué)基金培育項(xiàng)目“飛行器高雷諾數(shù)氣動(dòng)優(yōu)化及動(dòng)邊界問題高精度快速算法研究”（編號(hào)：91130019/A011702）

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

3.發(fā)表學(xué)術(shù)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(jí)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(guī)模問題，該文8次引用我們的模型，并稱其為 Xia-Yuan model.被頂級(jí)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(dú)立獲得了正交相似集凸包絡(luò)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(luò)，給出了一些等價(jià)刻畫，但是這些等價(jià)集合要么是無窮多個(gè)線性約束要么是非線性非凸約束，因而只能近似計(jì)算。我們巧妙構(gòu)造性證明了正交相似集的凸包絡(luò)可以由有限個(gè)線性矩陣不等式(LMI) 等價(jià)完整刻畫! Ding 和Wolkowicz的論文在09年《Mathematics of Operations Research》正式發(fā)表時(shí)用一個(gè)評(píng)論談及該項(xiàng)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(guān)于0-1與連續(xù)二次規(guī)劃關(guān)聯(lián)的一個(gè)公開問題。

[4]回答了Pinar和Teboulle于2006年在《RAIRO Operations Research》上提出的關(guān)于L1范數(shù)約束非凸二次規(guī)劃的兩個(gè)公開問題。

[5]Hiriart-Urruty于2007在《SIAM Review》提出了14個(gè)公開問題。其中第11個(gè)公開問題是問兩個(gè)二次正定型乘積的Legendre-Fenchel conjugate，在假定函數(shù)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(chuàng)性地提出參數(shù)Lagrangian對(duì)偶方法，目前在0-1二次規(guī)劃問題和界約束二次規(guī)劃問題上有成功的應(yīng)用。

[7]完美解決了等式約束S-lemma這一非凸二次優(yōu)化領(lǐng)域的基礎(chǔ)理論，論文被頂級(jí)期刊 《Mathematical Programming》錄用。

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

發(fā)表學(xué)術(shù)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(guī)劃松弛,中國運(yùn)籌學(xué)會(huì)第十屆學(xué)術(shù)交流會(huì)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(jì)問題的對(duì)偶方法, 運(yùn)籌學(xué)學(xué)報(bào), 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(yīng)用, 運(yùn)籌與模糊學(xué), 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)