Stochastic Augmented Lagrangian Method in Riemannian Shape Manifolds
提出一种在黎曼流形上求解带确定性约束的随机优化问题的增广拉格朗日方法，分析了收敛性，并应用于多形状优化问题。
Abstract In this paper, we present a stochastic augmented Lagrangian approach on (possibly infinite-dimensional) Riemannian manifolds to solve stochastic optimization problems with a finite number of deterministic constraints. We investigate the convergence of the method, which is based on a stochastic approximation approach with random stopping combined with an iterative procedure for updating Lagrange multipliers. The algorithm is applied to a multi-shape optimization problem with geometric constraints and demonstrated numerically.