Nonconvex Generalization of ADMM for Nonlinear Equality Constrained Problems

The ever-increasing demand for efficient and distributed optimization algorithms for large-scale data has led to the growing popularity of the Alternating Direction Method of Multipliers (ADMM). However, although the use of ADMM to solve linear equality constrained problems is well understood, we lacks a generic framework for solving problems with nonlinear equality constraints, which are common in practical applications (e.g., spherical constraints). To address this problem, we are proposing a new generic ADMM framework for handling nonlinear equality constraints, neADMM. After introducing the generalized problem formulation and the neADMM algorithm, the convergence properties of neADMM are discussed, along with its sublinear convergence rate $o(1/k)$, where $k$ is the number of iterations. Next, two important applications of neADMM are considered and the paper concludes by describing extensive experiments on several synthetic and real-world datasets to demonstrate the convergence and effectiveness of neADMM compared to existing state-of-the-art methods