TY - JOUR
T1 - A non-Euclidean gradient descent method with sketching for unconstrained matrix minimization
AU - Hallak, N.
AU - Teboulle, Marc
N1 - Publisher Copyright:
© 2019
PY - 2019/9
Y1 - 2019/9
N2 - We propose a method that incorporates a non-Euclidean gradient descent step with a generic matrix sketching procedure, for solving unconstrained, nonconvex, matrix optimization problems, in which the decision variable cannot be saved in memory due to its size, and the objective function is the composition of a vector function on a linear operator. The method updates the sketch directly without updating or storing the decision variable. Subsequence convergence, global convergence under the Kurdyka–Lojasiewicz property, and rate of convergence, are established.
AB - We propose a method that incorporates a non-Euclidean gradient descent step with a generic matrix sketching procedure, for solving unconstrained, nonconvex, matrix optimization problems, in which the decision variable cannot be saved in memory due to its size, and the objective function is the composition of a vector function on a linear operator. The method updates the sketch directly without updating or storing the decision variable. Subsequence convergence, global convergence under the Kurdyka–Lojasiewicz property, and rate of convergence, are established.
KW - Convergence analysis
KW - Matrix minimization
KW - Matrix sketching
KW - Non-Euclidean gradient method
UR - http://www.scopus.com/inward/record.url?scp=85070524921&partnerID=8YFLogxK
U2 - 10.1016/j.orl.2019.08.001
DO - 10.1016/j.orl.2019.08.001
M3 - מאמר
AN - SCOPUS:85070524921
VL - 47
SP - 421
EP - 426
JO - Operations Research Letters
JF - Operations Research Letters
SN - 0167-6377
IS - 5
ER -