An Average Curvature Accelerated Composite Gradient Method for Nonconvex Smooth Composite Optimization Problems

This paper presents an accelerated composite gradient (ACG) variant, referred to as the AC-ACG method, for solving nonconvex smooth minimization problems. As opposed well-known ACG variants that are based on either a known Lipschitz constant or sequence of maximum observed curvatures, current one is average all past curvatures. More specifically, uses positive multiple curvatures until previous iteration way estimate “function curvature” at point and then two resolvent evaluations compute next iterate. In contrast other variable estimation variants, e.g., ones curvature, always accepts aforementioned iterate regardless how poor turns out be. Finally, computational results presented illustrate efficiency both randomly generated real-world problem instances.