Abstract
In this paper, we propose an accelerated proximal point algorithm for the difference of convex (DC) optimization problem by combining the extrapolation technique with the proximal difference of convex algorithm. By making full use of the special structure of DC decomposition and the information of stepsize, we prove that the proposed algorithm converges at rate of O 1 / k 2 under milder conditions. The given numerical experiments show the superiority of the proposed algorithm to some existing algorithms.
Highlights
Difference of convex problem (DCP) is an important kind of nonlinear programming problems in which the objective function is described as the difference of convex (DC) functions
It is well known that the method to solve the DCP is the so-called difference of the convex algorithm (DCA) [14] in which the concave part is replaced by a linear majorant in the objective function and a convex optimization subproblem needs to be solved at each iteration
Gotoh et al [16] proposed the socalled proximal difference of the convex algorithm (PDCA) for solving DCP, in which the concave part is replaced by a linear majorant in each iteration and the smooth convex part is replaced by some techniques
Summary
Difference of convex problem (DCP) is an important kind of nonlinear programming problems in which the objective function is described as the difference of convex (DC) functions. Gotoh et al [16] proposed the socalled proximal difference of the convex algorithm (PDCA) for solving DCP, in which the concave part is replaced by a linear majorant in each iteration and the smooth convex part is replaced by some techniques. If the proximal mapping of the proper closed convex function can be computed, the subproblem involved in the PDCA can be solved efficiently. To accelerate the convergence rate of the proximal difference of the convex algorithm, researchers recall the well-known extrapolation technique to design some efficient algorithms [20,21,22,23,24]. If f is continuously differentiable, the (limiting) subdifferential reduces to the gradient of f and denoted by ∇f
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