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Mathematical Publications
Prof. Dr. sc. nat. Hoang Xuan Phu
Papers
| 74. |
N.-D. Hoang, N. K. Linh, and H. X. Phu::
Octagonal and Hexadecagonal Cut Algorithms for Finding the Convex Hull of Finite Sets with Linear Time Complexity,
Applied Mathematics and Computation, Vol. 481, Paper No. 128931, 19 pp., 2024.
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| 73. |
P. T. An and H. X. Phu:
Finding Globally Shortest Paths through a Sequence of Adjacent Triangles by the Method of Orienting Curves,
Journal of Global Optimization, Vol. 85, No. 4, pp. 1037–1063, 2023.
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| 72. |
D. T. Oanh, O. Davydov, and H. X. Phu:
Adaptive RBF-FD Method for Elliptic Problems with Point Singularities in 2D,
Applied Mathematics and Computation, Vol. 313, pp. 474-497, 2017.
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| 71. |
H. X. Phu:
Inner γ-Convex Functions in Normed Spaces,
Vietnam Journal of Mathematics, Vol. 43, No. 2, pp. 487-500, 2015.
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| 70. |
H. X. Phu and H. G. Bock:
A Common Regularization for Three River Discharge Optimization Problems,
Journal of Optimization Theory and Applications, Vol. 157, No. 1, pp. 199-228, 2013.
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| 69. |
H. X. Phu and V. M. Pho:
Some Properties of Boundedly Disturbed Strictly Convex Quadratic Functions,
Optimization, Vol. 61, No. 1, pp. 67-88, 2012.
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| 68. |
H. X. Phu, V. M. Pho, and P. T. An:
Maximizing Strictly Convex Quadratic Functions with Bounded Perturbation,
Journal of Optimization Theory and Applications, Vol. 149, No. 1, pp. 1-25, 2011.
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| 67. |
H. X. Phu and V. M. Pho:
Global Infimum of Strictly Convex Quadratic Functions with Bounded Perturbations,
Mathematical Methods of Operations Research, Vol. 72, No. 2, pp. 327-345, 2010.
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| 66. |
H. X. Phu: Minimizing Convex Functions with Bounded Perturbations,
SIAM Journal on Optimization, Vol. 20, No. 5, pp. 2709-2729, 2010.
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| 65. |
H. D. Minh, H. G. Bock, H. X. Phu, and J. P. Schlöder:
Fast Numerical Methods for Simulation of Chemically
Reacting Flows in Catalytic Monoliths,
in Modeling, Simulation and Optimization of Complex Processes,
Editors: H. G. Bock et al., pp. 371-380, Springer, Berlin-Heidelberg, 2008.
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| 64. |
H. X. Phu:
Supremizers of Inner γ-Convex Functions,
Mathematical Methods of Operations Research, Vol. 67, No. 2, pp. 207-222, 2008.
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| 63. |
H. X. Phu:
Outer Γ-Convexity in Vector Spaces,
Numerical Functional Analysis and Optimization, Vol. 25, No.
7&8, pp. 835-854, 2008.
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| 62. |
H. X. Phu:
Outer γ-Convexity and Inner γ-Convexity
of Disturbed Functions, Vietnam Journal of Mathematics,
Vol. 35, No. 1, pp. 107-119, 2007.
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| 61. |
H. X. Phu: Some Properties of Solution Sets to Nonconvex Quadratic Programming Problems,
Optimization, Vol. 56, No. 3, pp. 369-383, 2007.
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| 60. |
H. X. Phu: On Efficient Sets in R2,
Vietnam Journal of Mathematics, Vol. 33, No. 4, pp. 463-468, 2005.
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| 59. |
H. X. Phu and N. N. Hai: Some Analytical Properties of γ-Convex Functions in Normed Linear Spaces,
Journal of Optimization Theory and Applications, Vol. 126, No. 3, pp. 685-700, 2005.
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| 58. |
H. X. Phu: Some Basic Ideas of Rough Analysis,
in Proceedings of the Sixth Vietnamese Mathematical Conference, H. H. Khoai, D. T. Thi, D. L. Van (Eds.),
pp. 3-31, Hanoi National University Publishing House, Hanoi, 2005.
(pdf-file)
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| 57. |
H. X. Phu: On a Necessary Optimality Condition with Invexity,
Acta Mathematica Vietnamica, Vol. 29, No. 2, pp. 141-148, 2004. |
| 56. |
H. X. Phu: On some Badly-Solved Problems with Invexity, Acta
Mathematica Vietnamica, Vol. 29, No. 1, pp. 89-106, 2004. |
| 55. |
H. X. Phu: Is Invexity Weaker than Convexity? Vietnam Journal
of Mathematics, Vol. 32, No. 1, pp. 87-94, 2004. |
| 54. |
H. X. Phu: Approximate Fixed-Point Theorems for Discontinuous
Mappings, Numerical Functional Analysis and Optimization, Vol. 25, No.
1&2, pp. 119-136, 2004. |
| 53. |
H. X. Phu: Fixed-Point Property of Roughly Contractive
Mappings, Zeitschrift für Analysis und ihre Anwendungen, Vol. 22, No.
3, pp. 517-528, 2003. |
| 52. |
H. X. Phu, N. N. Hai and P. T. An: Piecewise Constant Roughly
Convex Functions, Journal of Optimization Theory and Applications,
Vol. 117, No. 2, pp. 415-438, 2003. |
| 51. |
H. X. Phu: Strictly and Roughly Convexlike Functions, Journal
of Optimization Theory and Applications, Vol. 117, No. 1, pp. 139-156,
2003. |
| 50. |
H. X. Phu: Some Geometrical Properties of Outer γ-Convex Sets,
Numerical Functional Analysis and Optimization,
Vol. 24, No. 3&4, pp. 303-309, 2003. |
| 49. |
H. X. Phu: Rough Convergence in Infinite Dimensional Normed
Spaces, Numerical Functional Analysis and Optimization, Vol. 24, No.
3&4, pp. 285-301, 2003. |
| 48. |
H. X. Phu: On Circumradii of Sets and Roughly Contractive
Mappings, Vietnam Journal of Mathematics, Vol. 31, No. 1, pp. 115-122, 2003.
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| 47. |
H. X. Phu: Rough Continuity of Linear Operators, Numerical
Functional Analysis and Optimization, Vol. 23, No. 1&2, pp. 139-146,
2002. |
| 46. |
H. X. Phu and T. D. Long: Orienting Method for Obstacle
Problems, Zeitschrift für Analysis und ihre Anwendungen, Vol. 21, No. 1, pp.
233-248, 2002. |
| 45. |
N. N. Hai and H. X. Phu: Boundedness of Symmetrically
γ-Convex Function, Acta Mathematica Vietnamica,
Vol. 26, No. 3, pp. 269-277, 2001. |
| 44. |
H. X. Phu: Rough Convergence in Normed Linear Spaces, Numerical
Functional Analysis and Optimization, Vol. 22, No. 1&2, pp. 201-224,
2001. |
| 43. |
H. X. Phu and N. D. Yen: On the Stability of Solutions to
Quadratic Programming Problems, Mathematical Programming, Ser. A, Vol.
89, No. 3, pp. 385-394, 2001. |
| 42. |
J. Hichert, A. Hoffmann, H. X. Phu and R. Reinhardt:
A Primal-Dual Integral Method in Global Optimization, Discussiones
Mathematicae - Differential Inclusions, Control and Optimization, Vol. 20,
No. 2, pp. 257-278, 2000. |
| 41. |
H. X. Phu and T. V. Truong: Invariant Property of Roughly
Contractive Mappings, Vietnam Journal of Mathematics, Vol. 28, No. 3, pp.
275-290, 2000. |
| 40. |
H. X. Phu, H. G. Bock, and S. Pickenhain: Rough
Stability of Solutions to Nonconvex Optimization Problems, in
Optimization, Dynamics, and Economic Analysis, Editors:
E. J. Dockner, R. F. Hartl, M. Luptacik, and
G. Sorger, pp. 22-35, Physica-Verlag (A Springer-Verlag Company),
Heidelberg New York, 2000. |
| 39. |
H. X. Phu and P. T. An: Outer γ-Convexity in Normed Linear Spaces,
Vietnam Journal of Mathematics, Vol. 27, No. 4, pp. 323-334, 1999. |
| 38. |
H. X. Phu and P. T. An: Stability of Generalized Convex
Functions with Respect to Linear Disturbances, Optimization, Vol. 46,
No. 4, pp. 381-389, 1999. |
| 37. |
N. N. Hai and H. X. Phu: Symmetrically γ-Convex Functions,
Optimization, Vol. 46, No. 1, pp. 1-23, 1999.
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| 36. |
H. X. Phu: Roughly Convex Functions, in Proceeding of the
Korea-Vietnam Joint Seminar ``Mathematical Optimization Theory and
Applications", Editors: Do Sang Kim and Pham Huu Sach, Pusan 1998, pp.
73-85. |
| 35. |
H. X. Phu, H. G. Bock and J. Schlöder: The Method of Orienting
Curves and Its Application for Manipulator Trajectory Planning,
Numerical Functional Analysis and Optimization, Vol. 18, No. 1&2, pp.
213-225, 1997. |
| 34. |
H. X. Phu: Six Kinds of Roughly Convex Functions, Journal of
Optimization Theory and Applications, Vol. 92, No. 2, pp. 357-375, 1997.
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| 33. |
J. Hichert, A. Hoffmann and H. X. Phu: Convergence Speed
of an Integral Method for Computing the Essential Supremum,
in Developments
in Global Optimization, Editors: I. M. Bomze,
T. Csendes, R. Horst, and P. M. Pardalos, pp. 153-170,
Kluwer Academic Publishers 1997. |
| 32. |
H. X. Phu and P. T. An: Stable Generalization of Convex
Functions, Optimization, Vol. 38, No. 4, pp. 309-318, 1996. |
| 31. |
H. X. Phu and A. Hoffmann: Essential Supremum and Supremum of
Summable Functions, Numerical Functional Analysis and Optimization,
Vol. 17, No. 1&2, pp. 167-180, 1996. |
| 30. |
H. X. Phu and N. N. Hai: Some Analytical Properties of
γ-Convex Functions on the Real Line, Journal of
Optimization Theory and Applications, Vol. 91, No.3, pp. 671-694, 1996.
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| 29. |
H. X. Phu, H. G. Bock and J. P. Schlöder: Extremal Solutions of
Some Constrained Control Problems, Optimization, Vol. 35, No. 4, pp.
345-355, 1995. |
| 28. |
H. X. Phu: Some Properties of Globally δ-Convex Functions,
Optimization, Vol. 35, No. 1, pp. 23-41, 1995.
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| 27. |
H. X. Phu and N. Dinh: Some Remarks on the
Method of Orienting Curves, Numerical Functional Analysis and
Optimization, Vol. 16, No. 5&6, pp. 755-763, 1995. |
| 26. |
H. X. Phu: γ-Subdifferential and γ-Convexity of Functions on a Normed Space,
Journal of Optimization Theory and Applications, Vol. 85, No. 3, pp. 649-676, 1995.
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| 25. |
H. X. Phu: Representation of Bounded Convex Sets by Rational Convex
Hull of Its γ-Extreme Points, Numerical Functional Analysis and
Optimization, Vol. 15, No. 7&8, pp. 915-920, 1994. |
| 24. |
H. X. Phu: γ-Subdifferential and γ-Convexity of Functions on the Real Line,
Applied Mathematics and Optimization, Vol. 27, pp. 145-160, 1993. |
| 23. |
N. Dinh and H. X. Phu: The Method of Orienting Curves and Its
Application to an Optimal Control Problem of Hydroelectric Power
Plants, Vietnam Journal of Mathematics (Tap chí Toán hoc), Vol. 20,
No. 2, pp. 40-53, 1992. |
| 22. |
N. Dinh and H. X. Phu: Solving a Class of Optimal Control Problems
Which Are Linear in the Control Variable by the Method of Orienting
Curves, Acta Mathematica Vietnamica, Vol. 17, No. 2, pp. 115-134,
1992. |
| 21. |
N. Dinh and H. X. Phu: Solving a Class of Regular Optimal Control
Problems with State Constraints by the Method of Orienting Curves,
Optimization, Vol. 25, No. 2&3, pp. 231-247, 1992. |
| 20. |
H. X. Phu: Method of Orienting Curves for Solving Optimal Control
Problems with State Constraints, Numerical Functional Analysis and
Optimization, Vol. 12, No. 1&2, pp. 173-211, 1991. |
| 19. |
H. X. Phu: Investigation of a Macroeconomic Model by the Method of
Region Analysis, Journal of Optimization Theory and Applications, Vol.
72, No. 2, pp. 319-332, 1992. |
| 18. |
H. X. Phu: The Method of Region Analysis and its Application for
Optimal Control Problems of Hydroelectric Power Plants, in
Proceedings of the Fourth European Consortium for Mathematics in
Industry, pp. 309-313, B.G. Teubner Stuttgart and Kluwer Academic
Publishers, the Netherlands, 1991. |
| 17. |
H. X. Phu: A Solution Method for Regular Optimal Control Problems
with State Constraints, Journal of Optimization Theory and
Applications, Vol. 62, No. 3, pp. 489-513, 1989. |
| 16. |
H. X. Phu: Optimal Control of a Hydroelectric Power Plant with
Unregulated Spilling Water, Systems & Control Letters, Vol. 10,
No. 1, pp. 131-139, 1988. |
| 15. |
H. X. Phu: Reguläre Aufgaben der optimalen Steuerung mit linearen
Zustandsrestriktionen, Zeitschrift für Analysis und ihre Anwendungen,
Vol. 7, No. 5, pp. 431-440, 1988. |
| 14. |
H. X. Phu: Investigation of Some Inventory Problems with Linear
Replenishment Cost by the Method of Region Analysis, in Optimal
Control Theory and Economic Analysis 3, Editor: G. Feichtinger,
North-Holland, Amsterdam, pp. 195-221, 1988. |
| 13. |
H. X. Phu: On a Linear Optimal Control Problem of a System with
Circuit-Free Graph Structure, International Journal of Control, Vol.
48, No. 5, pp. 1867-1882, 1988. |
| 12. |
H. X. Phu: Solution of Some High-Dimensional Linear Optimal Control
Problems by the Method of Region Analysis, International Journal of
Control, Vol. 47, No. 2, pp. 493-518, 1988. |
| 11. |
H. X. Phu: On Optimal Control of a Hydroelectric Power Plant,
Systems & Control Letters, Vol. 8, No. 3, pp. 281-288, 1987. |
| 10. |
H. X. Phu: A Method for Solving a Class of Optimal Control Problems
Which Are Linear in the Control Variable, Systems & Control
Letters, Vol. 8, No. 3, pp. 273-280, 1987. |
| 9. |
H. X. Phu: Some Necessary Conditions for Optimality for a Class of
Optimal Control Problems Which Are Linear in the Control Variable,
Systems & Control Letters, Vol. 8, No. 3, pp. 261-271, 1987. |
| 8. |
H. X. Phu: Ein konstruktives Lösungsverfahren für das Problem des
Inpolygons kleinsten Umfangs von J. Steiner, Optimization, Vol. 18,
No. 3, pp. 349-359, 1987. |
| 7. |
H. X. Phu: Zur Lösung eines Zermeloschen Navigationsproblems,
Optimization, Vol. 18, No. 2, pp. 225-236, 1987. |
| 6. |
H. X. Phu: Zur Lösung des Knickstab-Problems mit beschränkter
Ausbiegung, Zeitschrift für Analysis und ihre Anwendungen, Vol. 6, No.
4, pp. 371-384, 1987. |
| 5. |
H. X. Phu: Zur Lösung einer regulären Aufgabenklasse der optimalen
Steuerung im Großen mittels Orientierungskurven, Optimization, Vol.
18, No. 1, pp. 65-81, 1987. |
| 4. |
H. X. Phu: Einige notwendige Optimalitätsbedingungen für einfache
reguläre Aufgaben der optimalen Steuerung, Zeitschrift für Analysis
und ihre Anwendungen, Vol. 5, No. 5, pp. 465-475, 1986. |
| 3. |
H. X. Phu: Lösung einer eindimensionalen regulären Aufgaben der
optimalen Steuerung mit engen Zustandsbereichen anhand der Methode der
Bereichsanalyse, Optimization, Vol. 16, No. 3, pp. 431-438, 1985.
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| 2. |
H. X. Phu: Lineare Steuerungsprobleme mit engen
Zustandsbereichen, Optimization, Vol. 16, No. 2, pp. 273-284, 1985.
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| 1. |
H. X. Phu: Zur Stetigkeit der Lösung der adjungierten Gleichung bei
Aufgaben der optimalen Steuerung mit Zustandsbeschränkungen,
Zeitschrift für Analysis und ihre Anwendungen, Vol. 3, No. 6, pp. 527-539,
1984. |
Books
| 6. |
H. G. Bock, W. Jäger, E. Kostina, and H. X. Phu (Eds): Modeling, Simulation and Optimization
of Complex Processes HPSC 2018, Proceedings of the 7th International Conference on High Performance Scientific Computing, March 19-23, 2018, Hanoi, Vietnam.
Springer Nature 2021. ISBN 978-3-030-55239-8, ISBN 978-3-030-55240-4 (eBook). DOI 10.1007/978-3-319-67168-0. DOI 10.1007/978-3-030-55240-4.
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5. |
H. G. Bock, H. X. Phu, R. Rannacher, and J. P. Schlöder (Eds): Modeling, Simulation and Optimization
of Complex Processes HPSC 2015, Proceedings of the 6th International Conference on High Performance Scientific Computing, March 16-20, 2015, Hanoi, Vietnam.
Springer, 2017. ISBN 978-3-319-67167-3, ISBN 978-3-319-67168-0 (eBook). DOI 10.1007/978-3-319-67168-0.
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| 4. |
H. G. Bock, H. X. Phu, R. Rannacher, and J. P. Schlöder (Eds): Modeling, Simulation and Optimization
of Complex Processes HPSC 2012, Proceedings of the 5th International Conference on
High Performance Scientific Computing, March 5-9, 2012, Hanoi, Vietnam.
Springer, 2014. ISBN 978-3-319-09062-7, ISBN 978-3-319-09063-4 (eBook). DOI 10.1007/978-3-319-09063-4.
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| 3. |
H. G. Bock, H. X. Phu, R. Rannacher, and J. P. Schlöder (Eds): Modeling, Simulation and Optimization
of Complex Processes, Proceedings of the 4th International Conference on
High Performance Scientific Computing, March 2-6, 2009, Hanoi, Vietnam.
Springer, Berlin Heidelberg, 2012. ISBN 978-3-642-25706-3, e-ISBN 978-3-642-25707-0. DOI 10.1007/978-3-642-25707-0.
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| 2. |
H. G. Bock, E. Kostina, H. X. Phu, and R. Rannacher (Eds): Modeling, Simulation and Optimization
of Complex Processes, Proceedings of the 3rd International Conference on
High Performance Scientific Computing, March 6–10, 2006, Hanoi, Vietnam.
Springer, Berlin Heidelberg, 2008. ISBN: 978-3-540-79408-0, e-ISBN: 978-3-540-79409-7.
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| 1. |
H. G. Bock, E. Kostina, H. X. Phu, and R. Rannacher (Eds): Modeling, Simulation and Optimization
of Complex Processes, Proceedings of the 2nd International Conference on
High Performance Scientific Computing, March 10-14, 2003, Hanoi, Vietnam.
Springer, Berlin Heidelberg, 2005. ISBN 3-540-23027-0.
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Theses
| 3. |
H. X. Phu: Methode der Bereichsanalyse und Methode der
Orientierungskurven zur Lösung von Aufgaben optimaler Steuerung mit
Zustandsbeschränkungen, Habilitationsschrift, Leipzig, 1987. |
| 2. |
H. X. Phu: Methoden zur Lösung von Aufgaben der optimalen Steuerung
mit engen Zustandsbereichen, Dissertation, Universität Leipzig, 1983.
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| 1. |
H. X. Phu: Optimale Bilanzierung der Produktion am Fließband,
Diplomarbeit, Universität Leipzig, 1979.
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