On The Linear Convergence Of Difference-of-convex Algorithm With Error Bound

Difference-of-convex(DC)programming plays an key role in non-convex pro-gramming,and Difference-of-convex algorithm(DCA)is one of the effective algo-rithms for DC programming.Due to its fast computing speed,DC A is often used to deal with large-scale problems,which has recently become a hot research topic.After several decades of development,its convergence has been widely studied,but its rate of convergence is not well studied.In this paper,we analyse the convergence rate of DCA with error bounds.First of all,we introduce the concept of convex function and unconstrained optimization problems and their related properties,then we give a class of unconstrained DC programming which is discussed in the following paper with several assumptions,such as error bounds and isocost.By using first-order optimality condition and related inequalities,we proved the convergence of inertial DCA with error bounds.Moreover,we prove that the convergence rate of inertial DCA is linear.Finally,we give two numerical experiments:Least squares problems with regularizer and indefinite quadratic programming with box constraints.In the experiments,we draw the difference figures to illustrate the conclusion.