Optimization method with constraints and apparatus therefor

Abstract

In a method for determining a minimum value of an optimization function under constraints given by equations, a set of points which satisfy the constraints is regarded as a Riemannian manifold within a finite-dimensional real-vector space, the Riemannian manifold is approached from an initial position within the real-vector space. An exponential map regarding a geodesic line equation with respect to a tangent vector on the Riemannian manifold ends at a finite order, an approximate geodesic line is generated as a one-dimensional orbit. An approximate parallel-translation is performed on the tangent vector on the Riemannian manifold and on the orbit generated in the orbit generating step by finite-order approximation of the exponential map regarding the parallel translation of the tangent vector. By repeating the above-described procedure from the position at which a minimum value is given until the minimum value on the orbit converges, the solution of the optimization problem with constraints is determined using a simple calculation procedure.