This paper introduced a dynamical system (neural networks) algorithm for solving a least squares problem with orthogonality constraints, which has wide applications in computer vision and signal processing. A rigorous...This paper introduced a dynamical system (neural networks) algorithm for solving a least squares problem with orthogonality constraints, which has wide applications in computer vision and signal processing. A rigorous analysis for the convergence and stability of the algorithm was provided. Moreover, a so called zero extension technique was presented to keep the algorithm always convergent to the needed result for any randomly chosen initial data. Numerical experiments illustrate the effectiveness and efficiency of the algorithm.展开更多
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National Natural Science Foundation of China (No. 1990 10 18)
文摘This paper introduced a dynamical system (neural networks) algorithm for solving a least squares problem with orthogonality constraints, which has wide applications in computer vision and signal processing. A rigorous analysis for the convergence and stability of the algorithm was provided. Moreover, a so called zero extension technique was presented to keep the algorithm always convergent to the needed result for any randomly chosen initial data. Numerical experiments illustrate the effectiveness and efficiency of the algorithm.
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.
