Patent ID: 7587375

Claim:
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.