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


  • 2000- : Researcher (principal investigator since 2011), Institute of Mathematics, Vietnam Academy of Science and Technology, Vietnam
  • 2000 - 2015: University of Heidelberg, FU Berlin, International Centre for Theoretical Physics (ICTP), University of Lisbon: Postdoc, investigator, visiting researcher
  • 1990-2000: lecturer in Mathematics at Vinh University, Vietnam

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


List of publications in MathSciNet


List of recent publications
1Phan 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.
2T. 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.
3Le 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.
4Phan 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.
5Phan 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.
6Phan 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.
7Phan 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.
8Phan 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.
9Phan 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.
10Phan 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.
11Nguyen 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.
12Phan 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.
13Phan Thanh An, Le Hong Trang, A parallel algorithm based on convexity for the computing of Delaunay tessellation, Numerical Algorithms, 59 (2012), 347 -357.
14Hoang 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.
15N. 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.
16Phan 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
17Phan 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
18Phan 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.
19Phan 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.
20Phan Thanh An, Stability of generalized convexity and monotonicity. In: Mathematical modeling, simulation, visualization and e-learning, 193 - 200, Springer, Berlin, 2008.
21Phan Thanh An, Some computational aspects of Helly-type theorems. JNAIAM J. Numer. Anal. Ind. Appl. Math. 3 (2008), 269 - 274.
22Phan 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.
23Phan Thanh An, Helly-type theorems for roughly convex-like sets, Numer. Funct. Anal. Optim. 28 (2007), 553 - 558.
24Phan 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.
25Phan Thanh An, Stability of generalized monotone maps with respect to their characterizations, Optimization, 55 (2006),  289-299.
26Phan Thanh An, A new type of stable generalized convex functions. JIPAM. J. Inequal. Pure Appl. Math. 7 (2006), 10 pp.
27Phan Thanh An, Nonemptiness of approximate subdifferentials of midpoint $\delta$-convex functions, Numer. Funct. Anal. Optim. 26 (2005), 735 - 738.
28Phan Thanh An, Outer $\gamma$-convex functions on a normed space,  JIPAM.J. Inequal. Pure Appl. Math. 6 (2005), 8 pp.
29Phan Thanh An, Nguyen Ngoc Hai, δ-Convexity in Normed Linear Spaces, Numer. Funct. Anal. Optim. 25 (2004), 407 - 422.
30Hoang Xuan Phu, N.N. Hai, Phan Thanh An, Piecewise constant roughly convex functions, J. Optim. Theory Appl. 117 (2003), 415 - 438.
31Hoang Xuan Phu, Phan Thanh An, Outer $\gamma$-convexity in normed linear spaces. Vietnam J. Math. 27 (1999), 323 - 334.
32Hoang Xuan Phu, Phan Thanh An, Stability of generalized convex functions with respect to linear disturbances, Optimization 46 (1999), 381 - 389.
33Hoang Xuan Phu, Phan Thanh An, Stable generalization of convex functions. Optimization 3 (1996), 309 - 318.
1IMH20161101, Nguyen Ngoc Hai, Phan Thanh An, Phong Thi Thu Huyen, Shortest Paths along a Sequence of Line Segments in Euclidean Spaces.