A proximal algorithm with backtracked extrapolation for a class of structured fractional programming

In this paper, we consider a class of structured fractional minimization problems where the numerator part objective is sum convex function and Lipschitz differentiable (possibly) nonconvex function, while denominator function. By exploiting structure problem, propose first-order algorithm, namely, proximal-gradient-subgradient algorithm with backtracked extrapolation (PGSA_BE) for solving type optimization problem. It worth pointing out that there are few differences between our other popular extrapolations used in optimization. One such as follows: if new iterate obtained from extrapolated iteration satisfies backtracking condition, then will be replaced by one generated non-extrapolated iteration. We show any accumulation point sequence PGSA_BE critical problem regarded. addition, assuming some auxiliary functions satisfy Kurdyka-Łojasiewicz property, able to establish global convergence entire sequence, case locally differentiable, or its conjugate calmness condition. Finally, present preliminary numerical results illustrate efficiency PGSA_BE.