TY - JOUR
T1 - LINEAR CONVERGENCE ANALYSIS FOR A NONMONOTONE PROJECTED GRADIENT ALGORITHM SOLVING MULTIOBJECTIVE OPTIMIZATION PROBLEMS
AU - Zhao, Xiaopeng
AU - Jolaoso, Lateef O.
AU - Shehu, Yekini
AU - Yao, Jen Chih
N1 - Publisher Copyright:
© 2022 Yokohama Publications. All rights reserved.
PY - 2022
Y1 - 2022
N2 - We consider a nonmonotone projected gradient algorithm for solving convex constrained multiobjective optimization problems. This scheme was proposed recently in [N. S. Fazzio and M. L. Schuverdt, Optim. Lett., 13 (2019), pp. 1365-1379], where the strong convergence of the sequence generated by the algorithm to a weak Pareto optimal solution was established. In this work, under some approximate assumptions of the gradients of objective functions, we obtain better convergence property, i.e., the linear convergence result for the algorithm. We also give some numerical implementations of this method and compare with other recent method in the literature.
AB - We consider a nonmonotone projected gradient algorithm for solving convex constrained multiobjective optimization problems. This scheme was proposed recently in [N. S. Fazzio and M. L. Schuverdt, Optim. Lett., 13 (2019), pp. 1365-1379], where the strong convergence of the sequence generated by the algorithm to a weak Pareto optimal solution was established. In this work, under some approximate assumptions of the gradients of objective functions, we obtain better convergence property, i.e., the linear convergence result for the algorithm. We also give some numerical implementations of this method and compare with other recent method in the literature.
KW - Multiobjective optimization
KW - linear convergence
KW - nonmonotone line search
KW - projected gradient method
UR - http://www.scopus.com/inward/record.url?scp=85174894594&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:85174894594
SN - 1345-4773
VL - 23
SP - 2663
EP - 2675
JO - Journal of Nonlinear and Convex Analysis
JF - Journal of Nonlinear and Convex Analysis
IS - 11
ER -