2026/01/01 by Aclécio J. Santos, Jean C. Pereira, Guilherme V. Raffo
Computer Science · Engineering · Mathematics · #Advanced Optimization Algorithms Research #Numerical methods for differential equations #Tensor decomposition and applications #cs.SY #eess.SY #math.OC
paper · pdf · doi:10.1109/lcsys.2026.3709811
This is a preprint submitted to IEEE Control Systems Letters
openalex publication_date 2026/01/01 · arxiv created 2026/03/30 · openalex created_date 2026/07/04 · openalex updated_date 2026/08/01 · arxiv updated 2026/08/04
This paper proposes an interior-point framework for constrained optimization problems whose decision variables evolve on matrix Lie groups. The proposed method, termed the Matrix Lie Group Interior-Point Method (MLG-IPM), operates directly on the group structure using a minimal Lie algebra parametrization, avoiding redundant matrix representations and eliminating explicit dependence on Riemannian metrics. A primal-dual formulation is developed in which the Newton system is constructed through sensitivity and curvature matrices. Also, multiplicative updates are performed via the exponential map, ensuring intrinsic feasibility with respect to the group structure while maintaining strict positivity of slack and dual variables through a barrier strategy. A local analysis establishes quadratic convergence under standard regularity assumptions and characterizes the behavior under inexact Newton steps. Statistical comparisons against Riemannian Interior-Point Methods, specifically for optimization problems defined over the Special Orthogonal Group SO(n) and Special Linear Group SL(n), demonstrate that the proposed approach achieves higher success rates, fewer iterations, and superior numerical accuracy. Furthermore, its robustness under perturbations suggests that this method serves as a consistent and reliable alternative for structured manifold optimization.