Decentralized Optimization Over the Stiefel Manifold by an Approximate Augmented Lagrangian Function

In this paper, we focus on the decentralized optimization problem over Stiefel manifold, which is defined a connected network of $d$ agents. The objective an average local functions, and each function privately held by agent encodes its data. agents can only communicate with their neighbors in collaborative effort to solve problem. existing methods, multiple rounds communications are required guarantee convergence, giving rise high communication costs. contrast, paper proposes algorithm, called DESTINY, invokes single round per iteration. DESTINY combines gradient tracking techniques novel approximate augmented Lagrangian function. global convergence stationary points rigorously established. Comprehensive numerical experiments demonstrate that has strong potential deliver cutting-edge performance solving variety testing problems.