CONVERGENCE RATE OF GRADIENT DESCENT METHOD FOR MULTI-OBJECTIVE OPTIMIZATION

• 来源期刊: 计算数学（英文版）
• 关键词: Multi-objective optimization Gradient descent Convergence rate
• 年，卷（期）: 2019,（5）
• 页码范围: 689-703
• 页数: 15页
• 语种: 英文
• DOI: 10.4208/jcm.1808-m2017-0214

摘要

The convergence rate of the gradient descent method is considered for unconstrained multi-objective optimization problems (MOP).Under standard assumptions,we prove that the gradient descent method with constant stepsizes converges sublinearly when the objective functions are convex and the convergence rate can be strengthened to be linear if the objective functions are strongly convex.The results are also extended to the gradi ent descent method with the Armijo line search.Hence,we see that the gradient descentmethod for MOP enjoys the same convergence properties as those for scalar optimization.