Multipliers Correction Methods for Optimization Problems over the Stiefel Manifold

Understand

We propose a class of multipliers correction methods to minimize a differentiable function over the Stiefel manifold.

• The proposed methods combine a function value reduction step with a proximal correction step.
• The former one searches along an arbitrary descent direction in the Euclidean space instead of a vector in the tangent space of the Stiefel manifold.
• Meanwhile, the latter one minimizes a first-order proximal approximation of the objective function in the range space of the current iterate to make Lagrangian multipliers associated with orthogonality constraints symmetric at any accumulation point.