In this paper,we present a novel penalty model called ExPen for optimization over the Stiefel manifold.Different from existing penalty functions for orthogonality constraints,ExPen adopts a smooth penalty function wit...In this paper,we present a novel penalty model called ExPen for optimization over the Stiefel manifold.Different from existing penalty functions for orthogonality constraints,ExPen adopts a smooth penalty function without using any first-order derivative of the objective function.We show that all the first-order stationary points of ExPen with a sufficiently large penalty parameter are either feasible,namely,are the first-order stationary points of the original optimization problem,or far from the Stiefel manifold.Besides,the original problem and ExPen share the same second-order stationary points.Remarkably,the exact gradient and Hessian of ExPen are easy to compute.As a consequence,abundant algorithm resources in unconstrained optimization can be applied straightforwardly to solve ExPen.展开更多
基金the National Natural Science Foundation of China(Grant Nos.12125108,11971466,12288201,12021001,11991021)the Key Research Program of Frontier Sciences,Chinese Academy of Sciences(Grant No.ZDBS-LY-7022).
文摘In this paper,we present a novel penalty model called ExPen for optimization over the Stiefel manifold.Different from existing penalty functions for orthogonality constraints,ExPen adopts a smooth penalty function without using any first-order derivative of the objective function.We show that all the first-order stationary points of ExPen with a sufficiently large penalty parameter are either feasible,namely,are the first-order stationary points of the original optimization problem,or far from the Stiefel manifold.Besides,the original problem and ExPen share the same second-order stationary points.Remarkably,the exact gradient and Hessian of ExPen are easy to compute.As a consequence,abundant algorithm resources in unconstrained optimization can be applied straightforwardly to solve ExPen.
