Solving a Class of Nonsmooth Nonconvex Optimization Problems Via Proximal Alternating Linearization Scheme with Inexact Information

For optimization problems minimizing the sum of two nonconvex and nonsmooth functions, we propose an alternate linearization method with inexact data. In many practical optimization applications, only the inexact information of the function can be obtained. The core idea of this method is to add a quadratic function term to the nonconvex function(called local convexification of nonconvex function), and then to construct an approximate proximal point model. In each iteration, a series of iteration points are obtained by solving subproblems alternately. It can be proved that, in the sense of inexact oracles, these iteration points converge to the stable point of the original problem, and theoretically show that the algorithm has good convergent properties.