Quadratic optimization with orthogonality constraint: explicit Łojasiewicz exponent and linear convergence of retraction-based line-search and stochastic variance-reduced gradient methods

The problem of optimizing a quadratic form over an orthogonality constraint (QP-OC for short) is one of the most fundamental matrix optimization problems and arises in many applications. In this paper, we characterize the growth behavior of the objective function around the critical points of the QP-OC problem and demonstrate how such characterization can be used to obtain strong convergence rate results for iterative methods that exploit the...