TL;DR
It is proven that all limit points of the iterative sequences generated by the method satisfy the KKT conditions for the underlying optimization problem, and under certain assumptions, it is proved that this method achieves Q-linear convergence.
This paper proposes a novel Tensor Train (TT)-based tensor-on-tensor regression optimization framework for variable selection based on mode-1 hyperslice sparsity, and designs an alternating iterative algorithm equipped with a preconditioned metric to efficiently solve the proposed model.
High-dimensional extreme eigenvalue problems often arise from molecular vibrational models, electronic structure calculations, and quantum mechanics. Directly solving these problems suffers from the curse of dimensionality. Instead of tackling the problem in high-dimensional ambient space, we reformulate the problem th...
In this article, the problem of completing a tensor from some incomplete knowledge of its entries is treated by adopting a worst-case perspective, given the realistic assumption that the tensor's low-order ANOVA terms are dominant. We survey and leverage some recent all-purpose results from the field of Optimal Recover...
We study a class of weakly convex optimization problems in which the objective is the sum of a smooth convex term and a weakly convex term that may be non-smooth. To exploit this structure, we develop a splitting technique based on the alternating direction method of multipliers (ADMM), which decouples the minimization...
This work is concerned with the numerical computation of Gross-Pitaevskii ground states using the tensor train (TT) format. We regard the problem as the minimization of the Gross-Pitaevskii energy functional under a unit mass constraint, and propose a first-order Riemannian optimization scheme that preserves both the m...
In this paper, we consider the computation of $M$-eigenpairs of fourth order partially symmetric tensors arising from elasticity theory. First, a lifted fourth order tensor is constructed, and the original $M$-eigenvalue problem is reformulated as a parameterized generalized tensor eigenvalue problem under the $\mathbf...
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