許瑞麟   Ruey-Lin Sheu 職稱 教授 電話 06-2757575 轉 65150 傳真 06-2743191 辦公室 數學系館 408 電子郵件 rsheu[at]mail.ncku.edu.tw 個人網頁 http://www.math.ncku.edu.tw/~rsheu 專長學門 運籌學、演算法、二次規劃、分數型規畫、非線性分析 學歷     北卡羅萊納州立大學博士 (1992) 北卡羅萊納州立大學碩士 (1991) 清華大學學士 (1987) 經歷     1999–         成功大學數學系教授 2008–2012  成功大學數學系系主任 1993–1999  成功大學數學系副教授 1992–1993  AT&T 貝爾實驗室 Member of Technical Staff 編輯委員     2006 – present: Associate Editor, Journal of Global Optimization 2014 – 2017: Associate Editor, Taiwanese Journal of Mathematics 2013: Guest Editor (with J. Sun and W. Xing) of Pacific Journal of Optimization 2011: Guest Editor (with B. Mordukhovich and N. Popovici) of the symposium proceedings for GCM 10, a special issue published in Journal of Global Optimization 國際學術機構邀請演講     Econometric Institute, Erasmus School of Economics, Erasmus University, Rotterdam, The Netherlands, July 2019. Department of Mathematics, Beijing University of Posts and Telecommunications, Beijing, China, March 2019. Vietnam Institute for Advanced Study in Mathematics, Hanoi, Vietnam, January 2019. Research Institute for Mathematical Sciences (RIMS), Kyoto University, Kyoto, Japan, August 2017. Department of Mathematics, Faculty of Science, Chiang Mai University, Thailand, January 2016. School of Mathematics and System Sciences, Beihang University, Beijing, China, July 2015. Department of Industrial Engineering, North Carolina State University, USA, February 2015. Institute of Computational Mathematics and Engineering Computing, Chinese Academy of Sciences, Beijing, China, January 2015. Department of Mathematical Sciences, Tsing Hua University, Beijing, China, January 2015. Department of Mathematical Sciences, Tsing Hua University, Beijing, China, January 2015. College of Engineering and Natural Sciences, Sabanci University, Istanbul, Turkey, October 2014. Department of Decision Sciences, National University of Singapore, May 2013. Department of Mathematics, Izmir University of Economics, Turkey, July 2011. Graduate School of Science and Technology, Niigata University, Japan, December 2007. Centre for Informatics and Applied Optimization, University of Ballarat, Australia, August 2007. College of Engineering and Natural Sciences, Sabanci University, Istanbul, Turkey, April 2007. Department of Mathematical Sciences, Tsing Hua University, China, December 2006. Department of Mathematical Sciences, Tsing Hua University, Beijing, China, June 2006. Department of Industrial Engineering, North Carolina State University, USA, November 2004. 研究計畫     Characterizing the convexity of joint numerical range of quadratic mappings in real space, Ministry of Science and Technology, 2018 – 2020 (NTD 3,669,110). An analytic approach for the Celis-Dennis-Tapai problem Ministry of Science and Technology, 2016 – 2018 (NTD 2,260,500) Maximizing the sum of a generalized Rayleigh quotient and another Rayleigh quotient with applications National Science Council of Taiwan, 2014 – 2016 (NTD 2,521,500) On global minimization for a ratio of quadratic functions over quadratic constraints National Science Council of Taiwan, 2013 – 2014 (NTD 469,000) Estimation on the duality gap for the semidefinite programming relaxation of the standard quadratic program National Science Council of Taiwan, 2012 – 2013 (NTD 421,000) Extremal points of the generalized Ginzburg-Landau functionals National Science Council of Taiwan, 2011 – 2012 (NTD 365,000) Canonical duality for solving some classes of non-convex quadratic programming problems National Science Council of Taiwan, 2009 – 2011 (NTD 1,466,000) Canonical duality on local optimizers of quadratic functions with one quadratic constraint National Science Council of Taiwan, 2008 – 2009 (NTD 503,000) Theoretical and computational study on canonical duality for non-convex fractional program National Science Council of Taiwan, 2007 – 2008 (NTD 613,000) Primal-dual algorithm for solving min-max fractional programming National Science Council of Taiwan, 2005 – 2007 (NTD 978,000) Optimizing sum-of-ratios by stochastic search algorithm National Science Council of Taiwan, 2004 – 2005 (NTD 744,500) Minimization of an isotonic function composed of fractions National Science Council of Taiwan, 2003 – 2004 (NTD 452,600) Entropic regularization and generalized fractional programs of infinitely many ratios National Science Council of Taiwan, 2002 – 2003 (NTD 597,300) Computational efficiency of a new entropic-based interior point algorithm for minimax problems National Science Council of Taiwan, 2000 – 2002 (NTD 546,100) Optimization and statistical mechanics National Science Council of Taiwan, 2000 (NTD 513,500) Algorithms for min-max problems involving infinitely many convex functions National Science Council of Taiwan, 1999 – 2000 (NTD 385,800) Extensions and applications for certain convex min-max problems National Science Council of Taiwan, 1998 – 1999 (NTD 337,000) Using a combined row and column generation method for solving large scale linear program with applications National Science Council of Taiwan, 1997 – 1998 (NTD 243,800) Interior point methods for nonlinear convex programming National Science Council of Taiwan, 1996 – 1997 (NTD 241,000) Semi-infinite linear programming with large scale matrix computation National Science Council of Taiwan, 1995 – 1996 (NTD 326,500) Revised column generation for solving simulated crew scheduling problem National Science Council of Taiwan, 1993 – 1995 (NTD 200,000) 論文選輯 H-M Sun* and R. L. Sheu, 2019, “Minimum variance allocation among constrained intervals,” Journal of Global Optimization 74, 21 – 44. H. Q. Nguyen and R. L. Sheu*, 2019, “Geometric properties for level sets of quadratic functions,” Journal of Global Optimization, vol. 73, 349 – 369. Y. Hsia, R. L. Sheu*, and Y. Yuan, 2017, “Theory and application of p-regularized subproblems for p>2,” Optimization Methods and Software, vol. 32, no. 5, 1059 – 1077. Y. Xia, R. L. Sheu*, S. C. Fang, and W. Xing, 2017, “Double well potential function and its optimization in the n-dimensional real space -- part II,” Journal of Industrial and Management Optimization, vol. 13, no. 3, pp. 1307 – 1328. S. C. Fang, D. Y. Gao, G. X. Lin, R. L. Sheu*, and W. Xing, 2017, “Double well potential function and its optimization in the n-dimensional real space -- part I,” Journal of Industrial and Management Optimization, vol. 13, no. 3, pp. 1291 – 1305. Bong Nguyen, R. L. Sheu*, and Y. Xia, 2016, “An SDP approach for quadratic fractional problems with a two-sided quadratic constraint,” Optimization Methods and Software, vol. 31, no. 4, pp. 701 – 719. Y. Xia, S. Wang, and R. L. Sheu*, 2016, “S-lemma with equality and its applications,” Mathematical Programming, Series A., vol. 156, no. 1, pp. 513 – 547. Bong Nguyen, R. L. Sheu*, and Y. Xia, 2016, “Maximizing the sum of a generalized Rayleigh quotient and another Rayleigh quotient on the unit sphere via semidefinite programming,” Journal of Global Optimization, vol. 64, no. 2, pp. 399 – 416. X. Xing*, S. C. Fang, R. L. Sheu, and L. Zhang, 2015, “Canonical dual solutions to quadratic optimization over one quadratic constraint,’’ Asia-Pacific Journal of Operational Research, Vol. 32, No. 1, 1540007 (21 pages). Y. Hsia, G. X. Lin, and R. L. Sheu*, 2014, “A revisit to quadratic programming with one inequality quadratic constraint via matrix pencil,” Pacific Journal of Optimization, vol. 10, no. 3, pp. 461 - 481. J. Y. Lin*, H. J. Chen, and R. L. Sheu, 2013, “Augmented Lagrange primal-dual approach for generalized fractional programming problems,” Journal of Industrial and Management Optimization, vol. 9, no. 4, pp. 723 – 741. Y. Xia, R. L. Sheu*, X. Sun and D. Li, 2013, “Tightening a copositive relaxation for standard quadratic optimization problems,” Computational Optimization and Applications, vol. 55, pp. 379 – 398. J. M. Fen, G. X. Lin, R. L. Sheu*, and Y. Xia, 2012, “Duality and Solutions for Quadratic Programming over One Non-Homogeneous Quadratic Constraint,” Journal of Global Optimization, vol. 54, pp. 275 - 293. W. Xing*, S. C. Fang, R. L. Sheu, and Z. Wang, 2012, “A Canonical Dual Approach to Solving Linearly Constrained Quadratic Programs,” European Journal of Operational Research, vol. 218, no. 1, pp. 21– 27. Y. Xia, R. L. Sheu*, X. Sun, and D. Li, 2012, "Improved Estimation of Duality Gap in Binary Quadratic Programming Using a Weighted Distance Measure," European Journal of Operational Research, vol. 218, no. 2, pp. 351 – 357. J. Y. Lin and R. L. Sheu*, 2010, “Minimization of an isotonic function composed of fractions,” Journal of Optimization Theory and Applications, vol. 146, no 3, pp. 581 – 601. S. C. Fang*, D. Y. Gao, R. L. Sheu, and W. Xing, 2009, “Global Optimization for A Class of Fractional Programming Problems”, Journal of Global Optimization, vol. 45, no. 3, pp. 337 – 353. H. J. Chen, S. Schaible*, and R. L. Sheu, 2009, “Generic Algorithm for Generalized Fractional Programming,” Journal of Optimization Theory and Applications, vol. 141, no. 1, pp. 93 - 105. R. L. Sheu*, W. I. Wu and Ilker Birbil, 2008 “Solving the sum-of-ratios problem by stochastic search algorithm,” Journal of Global Optimization, vol. 42, no. 1, pp. 91-109. S. C. Fang, D. Y. Gao, R. L. Sheu*, and S. Y. Wu, 2008, “Canonical dual approach for solving quadratic integer programming problems”, Journal of Industrial and Management Optimization, vol. 4, no. 1, pp.125-142. J. Y. Lin, P. Manyem*, and R. L. Sheu, 2007, “Performance estimations of first fit algorithm for online bin packing with variable bin sizes and LIB constraints”, Pacific Journal of Optimization, vol. 3, no.3, pp. 511-527. R. L. Sheu*, M. J. Ting, and I. L. Wang, 2006, “Maximum flow problem in the distribution network”, Journal of Industrial and Management Optimization, vol. 2, no 3, pp. 237-254. J. Y. Lin and R. L. Sheu*, 2005, “Modified Dinkelbach-type algorithm for generalized fractional programming with infinitely many ratios”, Journal of Optimization Theory and Applications, vol. 126, no. 2, pp. 323-343. Ilker Birbil*, S. C. Fang and R.L. Sheu, 2004, “On the convergence of a population-based global optimization algorithm”, Journal of Global Optimization, vol. 30, no. 3, pp. 301 – 318. R. L. Sheu* and J. Y. Lin, 2004, “Solving continuous min-max problems by an iteratively entropic regularization method”, Journal of Optimization Theory and Applications, vol. 121, no.3, pp. 597-612. G. M. Jan, R.L. Sheu*, and S. Y. Wu, 2003, “Maximal feasibility problem for continuous linear inequalities”, Fuzzy Optimization and Decision Making, vol. 2, no. 4, pp. 297-316. R.L. Sheu*, 1999, “A generalized interior-point barrier function approach for smooth convex programming with linear constraints”, Journal of Information and Optimization Sciences, vol. 20, no. 2, pp. 187-202. R.L. Sheu* and S.Y. Wu, 1999, “Combined entropic-regularization and path-following method for solving finite convex minmax problems subject to infinitely many linear constraints”, Journal of Optimization Theory and Applications, vol. 101, pp. 167-190. J.C. Liu*, C.S. Wu, and R.L. Sheu, 1997, “Duality for fractional minimax programming”, Optimization 41, 117-133. J.C. Liu*, C.C. Lin and R.L. Sheu, 1997, “Optimality and duality for complex nondifferentiable fractional programming”, Journal of Mathematical Analysis and Applications, vol. 210, no. 2, pp. 804-824. Sheu, R.L.*, Wu, S.Y., and Fang, S.C., 1995, “A primal-dual infeasible-interior-point algorithm for linear semi-infinite programming,” Computers and Mathematics with Applications, vol. 29, no.8, pp. 7-18. Sheu, R.L.* and Fang, S.C., 1994, “On the generalized path-following methods for linear programming,” Optimization 30, 235-249. Sheu, R.L.* and Fang, S.C., 1993, “On the relationship of interior-point methods,” Internat. J. Math. & Math. Sci. vol. 16 no. 3, pp. 565-572. Sheu, R.L. and Fang, S.C.*, 1992, “Insights into the interior point methods,” ZOR 36, 227-257. 碩士班指導學生 畢業年度 姓名 107 蔡幸樺 106 林剛玄(博士)、吳佩穎、 劉正鴻、邱奕欽、劉兆敏 103 阮文蓬 (博士)、曾珮瑜 102 呂庭維、翁之翊 100 黎福全、黃萱華 99 林剛玄 98 陳慧如(博士)、馮若梅、 李依貞 97 朱書賢、陳銚壬 96 林詩珊 94 林仁彥(博士)、林威溢、 吳文祥 93 陳慧如、丁睦容、吳韋瑩 91 李政霖 90 吳昭寰 89 林仁彥 88 林士正 87 黃玉麟 86 蘇麗鳳、廖淑惠 85 李曉玲 83 何盈芬