Advanced Search
Article Contents
Article Contents

Solving Malfatti's high dimensional problem by global optimization

Abstract Related Papers Cited by
  • We generalize Malfatti's problem which dates back to 200 years ago as a global optimization problem in a high dimensional space. The problem has been formulated as the convex maximization problem over a nonconvex set. Global optimality condition by Strekalovsky [11] has been applied to this problem. For solving numerically Malfatti's problem, we propose the algorithm in [3] which converges globally. Some computational results are provided.
    Mathematics Subject Classification: Primary: 49K, 65K10; Secondary: 90C26.


    \begin{equation} \\ \end{equation}
  • [1]

    M. Andreatta, A. Bezdek and Jan P. Boroński., The problem of Malfatti: Two centuries of debate, The Mathematical Intelligencer, 33 (2011), 72-76.doi: 10.1007/s00283-010-9154-7.


    R. Enkhbat, Global optimization approach to Malfatti's problem, Accepted for JOGO and to appear in 2016.


    R. Enkhbat, An algorithm for maximizing a convex function over a simple set, Journal of Global Optimization, 8 (1996), 379-391.doi: 10.1007/BF02403999.


    H. Gabai and E. Liban, On Goldberg's inequality associated with the Malfatti problem, Math. Mag., 41 (1967), 251-252.


    M. Goldberg, On the original Malfatti problem, Math. Mag., 40 (1967), 241-247.


    G. A. Los, Malfatti's Optimization Problem [in Russian], Dep. Ukr. NIINTI, July 5, 1988.


    H. Lob and H. W. Richmond, On the solutions of the Malfatti problem for a triangle, Proc. London Math. Soc., 2 (1930), 287-301.doi: 10.1112/plms/s2-30.1.287.


    C. Malfatti, Memoria sopra una problema stereotomico, Memoria di Matematica e di Fisica della Societa italiana della Scienze,


    V. N. Nefedov, Finding the global maximum of a function of several variables on a set given by inequality constraints, Journal of Numerical Mathematics and Mathematical Physics, 27 (1987), 35-51.


    T. Saaty, Integer optimization methods and related extremal problems [Russian translation], Nauka, Moscow, 1973. 10 (1803), 235-244.


    A. S. Strekalovsky, On the global extrema problem, Soviet Math. Doklad, 292 (1987), 1062-1066.


    H. Tverberg, A generalization of Radon's theorem, Journal of the London Mathematical Society, 41 (1966), 123-128.


    V. A. Zalgaller, An inequality for acute triangles, Ukr. Geom. Sb., 34 (1991), 10-25.


    V. A. Zalgaller and G. A. Los, The solution of Malfatti's problem, Journal of Mathematical Sciences, 72 (1994), 3163-3177.doi: 10.1007/BF01249514.

  • 加载中

Article Metrics

HTML views() PDF downloads(359) Cited by(0)

Access History

Other Articles By Authors



    DownLoad:  Full-Size Img  PowerPoint