A Non-monotone Adaptive Scaled Gradient Projection Method for Orthogonality Constrained Problems

Optimization problems with orthogonality constraints are classical nonconvex nonlinear problems and have been widely applied in science and engineering. In order to solve this problem, we come up with an adaptive scaled gradient projection method. The method combines a scaling matrix that depends on the step size with some parameters that control the search direction. In addition, we consider the BB step size and combine a nonmonotone line search technique to accelerate the convergence speed of the proposed algorithm. Under the premise of non-monotonic, we prove the convergence of the algorithm. Also, the computation results proved the efficiency of the proposed algorithm.