Seminar Details
2016-02-23 (16.30) : A Forward-Backward Quasi-Newton algorithm for minimizing the sum of two nonconvex functions
At CORE (b-135)
Organized by Mathematical Engineering
Speaker :
Panos Patrinos (ESAT, KULeuven
)
Abstract :
In this talk we consider the problem of minimizing the sum of two nonconvex functions, one of which is smooth and the other prox-bounded and possibly nonsmooth. Such weak requirements on the functions significantly widen the range of applications compared to traditional splitting methods which typically rely on convexity. Our approach is based on the Forward-Backward Envelope (FBE), namely a locally Lipschitz continuous function whose stationary points coincide with those of the original problem. The proposed algorithm exhibits superlinear convergence rates under mild assumptions such as prox-regularity and second-order sufficiency conditions, by using exactly the same oracle information as forward-backward splitting to perform quasi-Newton steps. We show how our theoretical results are backed up by promising numerical simulations on large-scale problems, where the proposed algorithm with limited quasi-Newton updates dramatically outperforms, even in the convex case, popular algorithms like ADMM and the fast proximal gradient method. Joint seminar with the CORE Operations Research seminar series.