P. E. Gill, W. Murray and M. H. Wright, “Practical Optimization,” Academic Press, London, 1981.

has been cited by the following article:

• TITLE: Green’s Function Technique and Global Optimization in Reconstruction of Elliptic Objects in the Regular Triangle

  AUTHORS: Antonio Scalia, Mezhlum A. Sumbatyan

  KEYWORDS: Reconstruction, Global Optimization, Green's Function, Triangular Domain, Boundary Integral

  JOURNAL NAME: Applied Mathematics, Vol.2 No.3, March 24, 2011

  ABSTRACT: The reconstruction problem for elliptic voids located in the regular (equilateral) triangle is studied. A known point source is applied to the boundary of the domain, and it is assumed that the input data is obtained from the free-surface input data over a certain finite-length interval of the outer boundary. In the case when the boundary contour of the internal object is unknown, we propose a new algorithm to reconstruct its position and size on the basis of the input data. The key specific character of the proposed method is the construction of a special explicit-form Green's function satisfying the boundary condition over the outer boundary of the triangular domain. Some numerical examples demonstrate good stability of the proposed algorithm.