where q~ is a c losed, convex func t ion def ined on R n, having values in ~ and S is a c losed, convex set in ~n. We write S for the op t ima l so lu t ion set o f (1), S : = arg minxes cb(x) and assume this set to be non-empty , in o rde r tha t a p ro jec t ion o p e r a t i o n on to this set is well def ined. In o rde r to s impl i fy our analysis , let us define , b ~ ( x ) := ¢~(x )+~, (...

In this paper, we consider the problem of minimizing a continuously differentiable function on Stiefel manifold. To solve problem, develop geodesic-free proximal point algorithm equipped with Euclidean distance that does not require use Riemannian metric. The proposed method can be regarded as an iterative fixed-point repeatedly applies operator to initial point. addition, establish global conv...