Patent ID: 7197486

Claim:
A computer-implemented method performed by executing a computer-readable program stored in a computer-readable storage medium by a computer, for determining a minimum value of an optimization function under constraints given by equations, the method comprising the steps of: a projection step of regarding a set of points which satisfy the constraints as a Riemannian manifold within a finite-dimensional real-vector space and of projecting a given point onto the Riemannian manifold; a tangent vector updating/generating step of calculating a gradient of an optimization function as a point within the real-vector space and of updating/generating a tangent vector by projecting the obtained gradient vector onto a tangent space of the Riemannian manifold at the point on the Riemannian manifold projected in the projection step; a searching-direction-vector generating step of generating a searching-direction vector indicating a search direction on the basis of the tangent vector; an approximate geodesic line generating step of truncating an exponential map with respect to a geodesic line equation on the Riemannian manifold by a finite order and of generating an approximate geodesic line based on the searching-direction vector as a one-dimensional orbit obeying the truncated exponential map; an approximate parallel-translation step of performing approximate parallel-translation on the tangent vector on the Riemannian manifold and on the approximate geodesic line by finite-order approximation of the exponential map regarding the parallel translation of the tangent vector; and a minimum point determining step of determining a minimum point on the approximate geodesic line, which minimizes the optimization function, along the approximate geodesic line, wherein a sequence of all the steps is iterated by using the minimum point in a latest iteration as the given point in a succeeding iteration wherein the minimum point determined is used to simulate the behavior of a material object in a model of a physical phenomenon.