A Projected Gauss-Newton Variable Projection Method for Low Rank Approximations of Third Order Tensors and Extensions

报告摘要：This talk presents a novel parameterization for low-rank third-order tensor CP approximation, leveraging the variable projection technique to reduce the parameter space dimension by at least one-third. We reformulate the problem as a nonlinear least squares (NLS) optimization on a product of Oblique manifolds. To solve this, we propose a projected Gauss-Newton method, proving its global convergence and local quadratic convergence under mild assumptions. By incorporating selective reductions and reformulations, our implementation significantly improves computational efficiency. Numerical experiments indicate that our method matches the accuracy of state-of-the-art solvers (e.g., Tensor Toolbox and Tensorlab) while achieving an average speedup of dozens of times. We will also talk about some theoretical considerations on methods for the degenerate cases.

报告人简介：胡胜龙，国防科技大学教授，研究方向为非线性优化的理论与算法。部分研究成果发表在Math Program、Num Math、MOR、SIMAX、SIIMS、J Symb Comput等期刊。获得中国运筹学会青年科技奖等。入选教育部人才计划青年学者，主持国家自然科学基金、军科委、省自然科学基金多项。