We consider the difference-of-convex (DC) programming problems whose objective function is level-bounded. The classical DC algorithm (DCA) is well-known for solving this kind of problems, which returns a critical point. Recently, de Oliveira and Tcheo incorporated the inertial-force procedure into DCA (InDCA) for potential acceleration and preventing the algorithm from converging to a critical point which is not d(directional)-stationary. In this paper, based on InDCA, we propose two refined inertial DCA (RInDCA) with enlarged inertial step-sizes for better acceleration. We demonstrate the subsequential convergence of our refined versions to a critical point. In addition, by assuming the Kurdyka-Lojasiewicz (KL) property of the objective function, we establish the sequential convergence of RInDCA. Numerical simulations on image restoration problem show the benefit of enlarged step-size.
翻译:我们考虑的是目标功能受水平限制的电流(DC)编程问题。古典DC 算法(DCA)因解决这类问题而广为人知,这又是一个临界点。最近,De Oliveira和Tcheo将惯性力程序纳入DCA(InDCA),以潜在加速,防止算法相融合到非(直接)固定的临界点。在本文中,根据InDCA,我们建议两种精细的惯性DCA(RInDCA),使用扩大的惯性继级缩放,以更好地加速。我们显示了我们精细化的版本随后的趋同到临界点。此外,我们假设了目标功能的Kurdyka-Lojasiewicz(KL)属性,从而建立了RINDCA的相接轨趋同点。关于图像恢复问题的Numerical模拟显示扩大的递增规模的好处。