| US 7,587,375 B2 | ||
| Optimization method and optimization apparatus | ||
| Akira Asai, Atsugi (Japan); Shigeki Matsutani, Sagamihara (Japan); Katsuhiko Shinjo, Machida (Japan); Masanori Kuroda, Isehara (Japan); and Daichi Tsutsumi, Tokyo (Japan) | ||
| Assigned to Canon Kabushiki Kaisha, Tokyo (Japan) | ||
| Filed on Mar. 09, 2005, as Appl. No. 11/75,593. | ||
| Claims priority of application No. 2004-073299 (JP), filed on Mar. 15, 2004. | ||
| Prior Publication US 2005/0209898 A1, Sep. 22, 2005 | ||
| Int. Cl. G06E 1/00 (2006.01); G06E 3/00 (2006.01); G06G 7/00 (2006.01) | ||
| U.S. Cl. 706—19 | 8 Claims |
| 1. A computer implemented constrained optimization method for determining an interface shape, the constrained optimization
method comprising:
a computing unit (CPU) which performs linearly approximating a point of interest representing the interface shape of two types
of liquids, or a liquid and a gas, held in a container at a constant volume to a first hypersurface representing the constant
volume given as a constraint;
a computing unit (CPU) which performs finding an extreme value of an objective function representing an energy of contents
in the container by moving the point of interest along a quadratic curve having second-order osculation with a geodetic line
of a second hypersurface which is different from the first hypersurface with a constant, the second hypersurface and the geodetic
line passing through the point of interest and the geodetic line being directed in a direction in which a gradient vector
of the objective function is projected on a plane tangential to the second hypersurface;
a computing unit (CPU) which performs repeating the approximating the point of interest and the finding the extreme value
until a predetermined condition is satisfied;
a computing unit (CPU) which performs determining an interface shape corresponding to a current point of interest as a solution
of minimizing the energy of the contents in the container at the constant volume if the predetermined condition is satisfied;
and
a computing unit (CPU) which performs displaying on a display a graph representing the interface shape corresponding to the
points of interest repetitively obtained in the approximating the point of interest and the finding the extreme value.
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