Phan Thanh An

Associate Professor, Doctor

Department of Numerical Analysis and Scientific Computing
Research interests:

Computational Geometry, Generalized Convexity and Rough Convexity, Optimization, computational geometry

Office: Building A5, room 212
Tel: +84 24 37563474 / 212
Email: thanhan AT; thanhan AT
Personal homepage:

Education and academic degrees

  • 1990: Bachelor, Vinh University, Vietnam
  • 1999: PhD, Vinh University, Vietnam
  • 2009: Associate Professor of the Institute of Mathematics, Hanoi


  • 2017-2018: Visiting professor, University of São Paulo, Brasil
  • 2000- : Researcher (senior investigator since 2018), Institute of Mathematics, Vietnam Academy of Science and Technology, Vietnam
  • 2000 - 2015: University of Heidelberg, FU Berlin, International Centre for Theoretical Physics (ICTP): Postdoc, visiting researcher
  • 2009-2014: University of Lisbon: researcher
  • 1990-2000: lecturer in Mathematics at Vinh University, Vietnam

PhD. thesis supervision completed: 3, see the link

Research areas: Numerical Analysis, Optimization,  Scientific Computing, Computational geometry


List of publications in MathSciNet


List of recent publications
1Nguyễn Kiều Linh, Chanyoung Song, Joonghyun Ryu, Phan Thanh An, Hoang Nam Dung , Deok-Soo Kim, QuickhullDisk: A faster convex hull algorithm for disks, Applied Mathematics and Computation 363 (2019), 124626, (SCI-(E), Scopus).
2Phan Thanh An, Finding shortest paths in a sequence of triangles in 3D by the planar unfolding, Numerical Functional Analysis and Optimization, 40 (8) (2019), pp. 944-952, (Scopus, SCI(-E))
3Nguyễn Ngọc Hải, Phan Thanh An, Phong Thi Thu Huyen, Shortest paths along a sequence of line segments in Euclidean spaces, Journal of Convex Analysis, 26 (4) (2019) (Scopus, SCI(-E)).
4Phan Thanh An, Le Hong Trang, Computing approximately shortest descending paths on convex terrains via multiple shooting, Computational and Applied Mathematics, 37 (5) (2018), pp. 6499-6529. (SCI(-E), Scopus.
5Phan Thanh An, Finding Shortest Paths in a Sequence of Triangles in 3D by the Method of Orienting Curves, Optimization, 67 (2018), 159-177,SCI(-E); Scopus.
6T. V. Hoai, Phan Thanh An, N. N. Hai, Multiple shooting approach for computing approximately shortest paths on convex polytopes, Journal of Computational and Applied Mathematics, 317 (2017), 235–246, (SCI-E); Scopus.
7Le Hong Trang, Attila Kozma, Phan Thanh An, and Moritz Diehl, A sequential convex programming algorithm for minimizing a sum of Euclidean norms with non-convex constraints, Optimization Methods and Software, 31 (2016), 187-203, SCI(-E); Scopus.
8Phan Thanh An, Dinh Thanh Giang, A direct method for determining the lower convex hull of a finite point set in 3D, Proceedings of 3rd International Conference on Computer Science, Applied Mathematics and Applications - ICCSAMA 2015, May 11-13, Metz, France, Advances in Intelligent Systems and Computing, Springer, Vol. 358, 2015, pp. 15-26, Scopus.
9Phan Thanh An, D. T. Giang, L. H. Trang, An exact algorithm for minimizing a sum of Euclidean norms on rays in 2D and 3D, Numerical Functional Analysis and Optimization, 36 (2015), 405–418, SCI(-E), Scopus.
10Phan Thanh An, Nguyen Ngoc Hai, Tran Van Hoai, Le Hong Trang, On the performance of triangulation-based multiple shooting method for 2D shortest path problems, LNCS Transactions on Large Scale Data and Knowledge Centered Systems, Springer, 2014, 45-56, Scopus.
11Phan Thanh An, N. N. Hai, and T. V. Hoai, The role of graph for solving some geometric shortest path problems in 2D and 3D, Proceedings of the 5th FTRA International Conference on Computer Science and its Applications (CSA-13), Danang, Vietnam, December 18 - 21, 2013, 2013, Lecture Notes in Electrical Engineering (LNEE), Springer, Vol. 279, pp. 179-184, 2014, Scopus.
12Phan Thanh An, Le Hong Trang, An efficient convex hull algorithm for finite point sets in 3D based on the Method of Orienting Curves, Optimization, 62 (2013), 975-988, SCI(-E); Scopus.
13Phan Thanh An, Nguyen Ngoc Hai and Tran Van Hoai, The role of convexity for solving some shortest path problems in plane without triangulation, AIP Conference Proceedings, American Institute of Physics, NY, Vol. 1557 (2013), 89-93, Scopus.
14Phan Thanh An, Nguyen Ngoc Hai and Tran Van Hoai, Direct multiple shooting method for solving approximate shortest path problems, Journal of Computational and Applied Mathematics 244 (2013), 67 - 76, SCI(-E); Scopus.
15Nguyen Ngoc Hai, Phan Thanh An, A generalization of Blaschke's convergence theorem in metric spaces, Journal of Convex Analysis, 4 (2013), 1013 - 1024, preprint IMH2012/02/01, SCI(-E); Scopus.
16Phan Thanh An, T. V. Hoai, Incremental convex hull as an orientation to solving the shortest path problem, International Journal of Information and Electronics Engineering, 2 (2012), 652-655.
17Phan Thanh An, Le Hong Trang, A parallel algorithm based on convexity for the computing of Delaunay tessellation, Numerical Algorithms, 59 (2012), 347 -357,SCI(-E); Scopus.
18Hoang Xuan Phu, V. M. Pho, Phan Thanh An, Maximizing strictly convex quadratic functions with bounded perturbation, Journal of Optimization Theory and Applications, 149 (2011), 1-25, SCI(-E); Scopus.
19N. N. Hai, Phan Thanh An, Blaschke-type theorem and separation of disjoint closed geodesic convex sets, Journal of Optimazation Theory and Applications 3 (2011), 541 - 551, SCI(-E); Scopus.
20Phan Thanh An, D. T. Giang and N. N. Hai, Some computational aspects of geodesic convex sets in a simple polygon,  Numerical Functional Analysis and Optimization, 31 (2010), 221 -231
21Phan Thanh An, Method of orienting curves for determining the convex hull of a finite set of points in the plane,  Optimization,  59 (2010), 175 - 179
22Phan Thanh An, Reachable grasps on a polygon of a robot arm: finding convex ropes without triangulation,  International Journal of Robotics and Automation,  4 (2010), 304 - 310.
23Phan Thanh An, V. T. T. Binh, Stability of excess demand functions with respect to a strong version of Wald's axiom, Asia-Pacific Journal of Operational Research (APJOR) 26 (2009),  523-532.
24Phan Thanh An, Stability of generalized convexity and monotonicity. In: Mathematical modeling, simulation, visualization and e-learning, 193 - 200, Springer, Berlin, 2008.
25Phan Thanh An, Some computational aspects of Helly-type theorems. JNAIAM J. Numer. Anal. Ind. Appl. Math. 3 (2008), 269 - 274.
26Phan Thanh An, P. L. Na and N. Q. Chung, On parametric domain for asymptotic stability with probability one of zero solution of linear Ito stochastic differential equations, Ital. J. Pure Appl. Math., (2007), 129 - 138.
27Phan Thanh An, Helly-type theorems for roughly convex-like sets, Numer. Funct. Anal. Optim. 28 (2007), 553 - 558.
28Phan Thanh An, A modification of Graham's algorithm for determining the convex hull of a finite planar set, Ann. Math. Inform. 34 (2007), 3 - 8.
29Phan Thanh An, Stability of generalized monotone maps with respect to their characterizations, Optimization, 55 (2006),  289-299.
30Phan Thanh An, A new type of stable generalized convex functions. JIPAM. J. Inequal. Pure Appl. Math. 7 (2006), 10 pp.
31Phan Thanh An, Nonemptiness of approximate subdifferentials of midpoint $\delta$-convex functions, Numer. Funct. Anal. Optim. 26 (2005), 735 - 738.
32Phan Thanh An, Outer $\gamma$-convex functions on a normed space,  JIPAM.J. Inequal. Pure Appl. Math. 6 (2005), 8 pp.
33Phan Thanh An, Nguyen Ngoc Hai, δ-Convexity in Normed Linear Spaces, Numer. Funct. Anal. Optim. 25 (2004), 407 - 422.
34Hoang Xuan Phu, N.N. Hai, Phan Thanh An, Piecewise constant roughly convex functions, J. Optim. Theory Appl. 117 (2003), 415 - 438.
35Hoang Xuan Phu, Phan Thanh An, Outer $\gamma$-convexity in normed linear spaces. Vietnam J. Math. 27 (1999), 323 - 334.
36Hoang Xuan Phu, Phan Thanh An, Stability of generalized convex functions with respect to linear disturbances, Optimization 46 (1999), 381 - 389.
37Hoang Xuan Phu, Phan Thanh An, Stable generalization of convex functions. Optimization 3 (1996), 309 - 318.
1IMH20200601, Phan Thanh An, Phong Thi Thu Huyen, Nguyen Thi Le, A Modified Graham’s Scan Algorithm for Finding the Smallest Connected Orthogonal Convex Hull of a Finite Planar Point Set