Coordinate Descent Methods for DC Minimization: Optimality Conditions and Global Convergence

Difference-of-Convex (DC) minimization, referring to the problem of minimizing difference two convex functions, has been found rich applications in statistical learning and studied extensively for decades. However, existing methods are primarily based on multi-stage relaxation, only leading weak optimality critical points. This paper proposes a coordinate descent method class DC functions sequential nonconvex approximation. Our approach iteratively solves one-dimensional subproblem globally, it is guaranteed converge coordinate-wise stationary point. We prove that this new condition always stronger than standard point directional under mildlocally bounded nonconvexity assumption. For comparisons, we also include naive variant approximation our study. When objective function satisfies globally assumption Luo-Tseng error bound assumption, achieve Q-linear convergence rate. Also, many interest, show can be computed exactly efficiently using breakpoint searching method. Finally, have conducted extensive experiments several tasks superiority approach.