TY - JOUR
T1 - A simplified view of first order methods for optimization
AU - Teboulle, Marc
N1 - Publisher Copyright:
© 2018, Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society.
PY - 2018/7/1
Y1 - 2018/7/1
N2 - We discuss the foundational role of the proximal framework in the development and analysis of some iconic first order optimization algorithms, with a focus on non-Euclidean proximal distances of Bregman type, which are central to the analysis of many other fundamental first order minimization relatives. We stress simplification and unification by highlighting self-contained elementary proof-patterns to obtain convergence rate and global convergence both in the convex and the nonconvex settings, which in turn also allows to present some novel results.
AB - We discuss the foundational role of the proximal framework in the development and analysis of some iconic first order optimization algorithms, with a focus on non-Euclidean proximal distances of Bregman type, which are central to the analysis of many other fundamental first order minimization relatives. We stress simplification and unification by highlighting self-contained elementary proof-patterns to obtain convergence rate and global convergence both in the convex and the nonconvex settings, which in turn also allows to present some novel results.
KW - Convex and nonconvex minimization
KW - Descent Lemma
KW - First order algorithms
KW - Kurdyka–Łosiajewicz property
KW - Non-Euclidean Bregman distance
KW - Proximal framework
UR - http://www.scopus.com/inward/record.url?scp=85046761883&partnerID=8YFLogxK
U2 - 10.1007/s10107-018-1284-2
DO - 10.1007/s10107-018-1284-2
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AN - SCOPUS:85046761883
SN - 0025-5610
VL - 170
SP - 67
EP - 96
JO - Mathematical Programming
JF - Mathematical Programming
IS - 1
ER -