Extrapolated Proximal Subgradient Algorithms for Nonconvex and Nonsmooth Fractional Programs

In this paper, we consider a broad class of nonsmooth and nonconvex fractional programs, where the numerator can be written as sum continuously differentiable convex function whose gradient is Lipschitz continuous proper lower semicontinuous (possibly nonconvex) function, denominator weakly over constraint set. This model problem includes composite optimization problems studied extensively lately, encompasses many important modern arising from diverse areas such recently proposed scale invariant sparse signal reconstruction in processing. We propose proximal subgradient algorithm with extrapolations for solving show that iterated sequence generated by bounded any its limit points stationary point problem. The choice our extrapolation parameter flexible popular adopted restarted Fast Iterative Shrinking-Threshold Algorithm (FISTA). By providing unified analysis framework descent methods, establish convergence full under assumption suitable merit satisfies Kurdyka--{\L}ojasiewicz (KL) property. particular, exhibits linear Rayleigh quotient spherical constraint. case maximum finitely functions, also an enhanced extrapolated guaranteed to stronger notion Finally, illustrate methods both analytical simulated numerical examples.