A new variant of the memory gradient method for unconstrained optimization

Zheng, Yue; Wan, Zhongping

doi:10.1007/s11590-011-0355-6

Cited by 7 publications

(2 citation statements)

References 15 publications

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“…where the last inequality holds because the definition of ψ(•, •) as in (5). Thus, by (34), (35) and the definitions of α k given in (24), we have…”

Section: Convergence Analysismentioning

confidence: 89%

“…Narushima and Yabe [33] introduced a new memory gradient method that also uses historical direction information and then derived the global convergence of the method under appropriate conditions. Other methods that use historical iterative information at the current step to improve the algorithmic performance have been reported in [34][35][36][37]. In summary, it would be a good choice to design new algorithms based on historical iterative information in scalar optimization.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Memory gradient method for multiobjective optimization

Chen¹,

Yang²,

Zhao³

2022

Preprint

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In this paper, we propose a new descent method, termed as multiobjective memory gradient method, for finding Pareto critical points of a multiobjective optimization problem. The main thought in this method is to select a combination of the current descent direction and past multi-step iterative information as a new search direction and to obtain a stepsize by virtue of two types of strategies. It is proved that the developed direction with suitable parameters always satisfies the sufficient descent condition at each iteration. Based on mild assumptions, we obtain the global convergence and the rates of convergence for our method. Computational experiments are given to demonstrate the effectiveness of the proposed method.

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“…where the last inequality holds because the definition of ψ(•, •) as in (5). Thus, by (34), (35) and the definitions of α k given in (24), we have…”

Section: Convergence Analysismentioning

confidence: 89%