TY - GEN
T1 - A new envelope function for nonsmooth DC optimization
AU - Themelis, Andreas
AU - Hermans, Ben
AU - Patrinos, Panagiotis
N1 - Funding Information:
1Andreas Themelis and Panagiotis Patrinos are with the Department of Electrical Engineering (ESAT-STADIUS) – KU Leuven, Kasteelpark Aren-berg 10, 3001 Leuven, Belgium. This work was supported by the Research Foundation Flanders (FWO) research projects G086518N, G086318N, and G0A0920N; Research Council KU Leuven C1 project No. C14/18/068; Fonds de la Recherche Scientifique — FNRS and the Fonds Wetenschap-pelijk Onderzoek — Vlaanderen under EOS project no 30468160 (SeLMA). 2Ben Hermans is with the MECO Research Team, Department of Mechanical Engineering, KU Leuven, and Flanders Make - DMMS_M, Leuven, Belgium. His research benefits from KU Leuven-BOF PFV/10/002 Centre of Excellence: Optimization in Engineering (OPTEC), from project G0C4515N of the Research Foundation - Flanders (FWO - Flanders), from Flanders Make ICON: Avoidance of collisions and obstacles in narrow lanes, and from the KU Leuven Research project C14/15/067: B-spline based certificates of positivity with applications in engineering.
Publisher Copyright:
© 2020 IEEE.
PY - 2020/12/14
Y1 - 2020/12/14
N2 - Difference-of-convex (DC) optimization problems are shown to be equivalent to the minimization of a Lipschitz-differentiable envelope. A gradient method on this surrogate function yields a novel (sub)gradient-free proximal algorithm which is inherently parallelizable and can handle fully nonsmooth formulations. Newton-type methods such as L-BFGS are directly applicable with a classical linesearch. Our analysis reveals a deep kinship between the novel DC envelope and the forward-backward envelope, the former being a smooth and convexity-preserving nonlinear reparametrization of the latter.
AB - Difference-of-convex (DC) optimization problems are shown to be equivalent to the minimization of a Lipschitz-differentiable envelope. A gradient method on this surrogate function yields a novel (sub)gradient-free proximal algorithm which is inherently parallelizable and can handle fully nonsmooth formulations. Newton-type methods such as L-BFGS are directly applicable with a classical linesearch. Our analysis reveals a deep kinship between the novel DC envelope and the forward-backward envelope, the former being a smooth and convexity-preserving nonlinear reparametrization of the latter.
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U2 - 10.1109/CDC42340.2020.9304514
DO - 10.1109/CDC42340.2020.9304514
M3 - Conference contribution
AN - SCOPUS:85095312985
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 4697
EP - 4702
BT - 2020 59th IEEE Conference on Decision and Control, CDC 2020
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 59th IEEE Conference on Decision and Control, CDC 2020
Y2 - 14 December 2020 through 18 December 2020
ER -