论文标题
乘数校正方法，用于在Stiefel歧管上优化问题
Multipliers Correction Methods for Optimization Problems over the Stiefel Manifold
论文作者
论文摘要
我们提出了一类乘数校正方法，以最大程度地减少在Stiefel歧管上的可区分函数。所提出的方法将功能值降低步骤与近端校正步骤结合在一起。前者沿着欧几里得空间中的任意下降方向进行搜索，而不是在Stiefel歧管的切线空间中的向量。同时，后者将目标函数的一阶近端近似在当前迭代的范围内近近近似，以使与正交性约束相关的拉格朗日乘数在任何累积点对称。已为提出的方法建立了全球收敛。初步数值实验表明，新方法在解决各种测试问题方面明显优于其他最先进的一阶方法。
We propose a class of multipliers correction methods to minimize a differentiable function over the Stiefel manifold. The proposed methods combine a function value reduction step with a proximal correction step. The former one searches along an arbitrary descent direction in the Euclidean space instead of a vector in the tangent space of the Stiefel manifold. Meanwhile, the latter one minimizes a first-order proximal approximation of the objective function in the range space of the current iterate to make Lagrangian multipliers associated with orthogonality constraints symmetric at any accumulation point. The global convergence has been established for the proposed methods. Preliminary numerical experiments demonstrate that the new methods significantly outperform other state-of-the-art first-order approaches in solving various kinds of testing problems.
