TY - JOUR
T1 - Convergence of the Peaceman-Rachford Splitting Method for a Class of Nonconvex Programs
AU - Chao , Miantao
AU - Han , Deren
AU - Cai , Xingju
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 2
SP - 438
EP - 460
PY - 2021
DA - 2021/01
SN - 14
DO - http://doi.org/10.4208/nmtma.OA-2020-0063
UR - https://global-sci.org/intro/article_detail/nmtma/18606.html
KW - Kurdyka-Łojasiewicz inequality, Peaceman-Rachford splitting method, nonconvex,
strongly convex, Douglas-Rachford splitting method.
AB - <p style="text-align: justify;">In this paper, we analyze the convergence of the Peaceman-Rachford splitting method (PRSM) for a type of nonconvex and nonsmooth optimization with
linear constraints, whose objective function is the sum of a proper lower semicontinuous function and a strongly convex differential function. When a suitable penalty
parameter is chosen and the iterative point sequence is bounded, we show the global
convergence of the PRSM. Furthermore, under the assumption that the associated
function satisfies the Kurdyka-Łojasiewicz property, we prove the strong convergence
of the PRSM. We also provide sufficient conditions guaranteeing the boundedness of
the generated sequence. Finally, we present some preliminary numerical results to
show the effectiveness of the PRSM and also give a comparison with the Douglas-Rachford splitting method.</p>