36 research outputs found
Nonlinear Analysis: Algorithm, Convergence, and Applications 2014
Department of Applied Mathematic
A Self-Adjusting Spectral Conjugate Gradient Method for Large-Scale Unconstrained Optimization
This paper presents a hybrid spectral conjugate gradient method for large-scale unconstrained optimization, which possesses a self-adjusting property. Under the standard Wolfe conditions, its global convergence result is established. Preliminary numerical results are reported on a set of large-scale problems in CUTEr to show the convergence and efficiency of the proposed method
Multi-mode Tensor Train Factorization with Spatial-spectral Regularization for Remote Sensing Images Recovery
Tensor train (TT) factorization and corresponding TT rank, which can well
express the low-rankness and mode correlations of higher-order tensors, have
attracted much attention in recent years. However, TT factorization based
methods are generally not sufficient to characterize low-rankness along each
mode of third-order tensor. Inspired by this, we generalize the tensor train
factorization to the mode-k tensor train factorization and introduce a
corresponding multi-mode tensor train (MTT) rank. Then, we proposed a novel
low-MTT-rank tensor completion model via multi-mode TT factorization and
spatial-spectral smoothness regularization. To tackle the proposed model, we
develop an efficient proximal alternating minimization (PAM) algorithm.
Extensive numerical experiment results on visual data demonstrate that the
proposed MTTD3R method outperforms compared methods in terms of visual and
quantitative measures.Comment: 21 page