Inexact Boosted Difference of Convex Algorithm

Abstract

In this paper, we propose the Inexact Difference of Convex Algorithm (iBDCA), an inexact variant of the Boosted Difference of Convex Functions Algorithm (BDCA), to solve an optimization problem involving the difference of two strongly convex functions, where both components of the DC function are assumed to be differentiable and the gradient of the first component is Lipschitz continuous. The proposed algorithm consists of two main steps: First, we employ a gradient descent-based scheme to find an approximate solution to a subproblem related to the convex part of the DC function; second, this approximate point is then used to compute a suitable step size for the next iteration. The convergence and convergence rate of the iterates and the value sequence of the objective function to the optimal solution and the optimal value are established, along with the complexity of the subproblem.