TY - GEN
T1 - Convergence rates of inertial splitting schemes for nonconvex composite optimization
AU - Johnstone, Patrick R.
AU - Moulin, Pierre
N1 - Publisher Copyright:
© 2017 IEEE.
PY - 2017/6/16
Y1 - 2017/6/16
N2 - We study the convergence properties of a general inertial first-order proximal splitting algorithm for solving nonconvex nonsmooth optimization problems. Using the Kurdyka-Łojaziewicz (KL) inequality we establish new convergence rates which apply to several inertial algorithms in the literature. Our basic assumption is that the objective function is semialgebraic, which lends our results broad applicability in the fields of signal processing and machine learning. The convergence rates depend on the exponent of the 'desingularizing function' arising in the KL inequality. Depending on this exponent, convergence may be finite, linear, or sublinear and of the form O(k-p) for p > 1.
AB - We study the convergence properties of a general inertial first-order proximal splitting algorithm for solving nonconvex nonsmooth optimization problems. Using the Kurdyka-Łojaziewicz (KL) inequality we establish new convergence rates which apply to several inertial algorithms in the literature. Our basic assumption is that the objective function is semialgebraic, which lends our results broad applicability in the fields of signal processing and machine learning. The convergence rates depend on the exponent of the 'desingularizing function' arising in the KL inequality. Depending on this exponent, convergence may be finite, linear, or sublinear and of the form O(k-p) for p > 1.
KW - Inertial forward-backward splitting
KW - Kurdyka-Łojaziewicz Inequality
KW - convergence rate
KW - first-order methods
KW - heavy-ball method
UR - http://www.scopus.com/inward/record.url?scp=85023750260&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85023750260&partnerID=8YFLogxK
U2 - 10.1109/ICASSP.2017.7953051
DO - 10.1109/ICASSP.2017.7953051
M3 - Conference contribution
AN - SCOPUS:85023750260
T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
SP - 4716
EP - 4720
BT - 2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017 - Proceedings
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017
Y2 - 5 March 2017 through 9 March 2017
ER -