Abstract:

The problem of the descent algorithm along geodesic on Riemannian manifolds is provided. A technique for the optimization algorithm for the differentiable function on differentiable manifolds is given. The constrained optimization problem is converted to the unconstrained case with the special choices of coordinate transformation and the optimality condition for the constrained optimization problem is given. Moreover, a mapping gradient method is developed and linear convergence of the mapping gradient method is established.

Key words: differentiable manifold, optimization algorithms, coordinate transformation