Quadratic Equality Constrained Least Squares: Low-complexity ADMM for Global Optimality

Journal article, 2026

This letter addresses the quadratic equality constrained least squares (QEC-LS) problem, a class of non-convex optimization problems that arise in various signal processing and communication applications. We revisit the alternating direction method of multipliers (ADMM) approach to QEC-LS problem and investigate its convergence and efficiency. Despite the inherent non-convexity, the proposed ADMM algorithm is proved to converge globally only requiring the quadratic term equal to a positive constant. Numerical results demonstrate that our method achieves global optimality with significantly reduced complexity compared to existing approaches such as semidefinite relaxation and primal-dual methods.