Inertial Forward—Reflected—Backward Splitting Method with Linesearch for Nonconvex Split Feasibility Problem

This paper studies the nonconvex split feasibility problem (NCSFP) which can be applied widely in some practical problems, such as compressed sensing, intensity–modulated radiation therapy, matrix factorization, outlier detection problem, and sudoku puzzle. The NCSFP is transformed into an unconstrained optimization problem whose objective function is nonconvex and nonsmooth. Then, we first adopt the framework of Malitsky—Tam forward—reflected—backward splitting method, together with inertial strategy to accelerate the convergence and a linesearch procedure to avoid computing the Lipschitz constant of some related mapping simultaneously. By assuming the semi–algebraic sets, we demonstrate that each bounded sequence generated by inertial forward—reflected—backward splitting method with a linesearch globally converges to a critical point and obtain the linear convergence rates. Numerical experiments validate rationality and effectiveness of the proposed algorithm.