求解无约束优化问题的改进q-信赖域算法

doi:10.15960/j.cnki.issn.1007-6093.2026.02.016

运筹学学报（中英文） ›› 2026, Vol. 30 ›› Issue (2): 209-224.doi: 10.15960/j.cnki.issn.1007-6093.2026.02.016

求解无约束优化问题的改进q-信赖域算法

仇英茗, 彭建文^†

重庆师范大学数学科学学院, 重庆 401331

收稿日期:2023-05-19 出版日期:2026-06-15 发布日期:2026-06-12
通讯作者: 彭建文 E-mail:jwpeng168@hotmail.com
基金资助:
国家自然科学基金面上项目 (No. 12271071), 国家自然科学基金重大项目 (No. 11991024),重庆英才·创新创业领军人才·创新创业示范团队项目 (No. CQYC20210309536),重庆英才包干制项目 (No. cstc2022ycjh-bgzxm0147), 重庆市高校创新研究群体项目 (No. CXQT20014),重庆市自然科学基金项目 (No. cstc2021jcyj-msxmX0300)

Improved q-trust region algorithm for unconstrained optimization problems

QIU Yingming, PENG Jianwen^†

School of Mathematics and Sciences, Chongging Normal University, Chongging 401331, China

Received:2023-05-19 Online:2026-06-15 Published:2026-06-12

摘要/Abstract

摘要： 本文提出了求解无约束优化问题的改进$q$-信赖域算法。该算法具有新的信赖域半径更新规则。在函数连续$q$-可微等条件下,我们建立了求解无约束优化问题的改进$q$-信赖域算法的收敛性。最后,数值实验表明,我们的算法是有效的。与Zhou提出的改进信赖域算法相比,我们提出的改进$q$-信赖域算法不仅可以更快地迭代到最优点,还可以解决具有多个最优点的优化问题。本文所得的结果推广和改进了文献中的一些已有结果。

关键词: $q$-导数, 信赖域算法, 信赖域半径, 无约束优化, 连续$q$-可微

Abstract: In this paper, we propose an improved $q$-trust region algorithm for solving unconstrained optimization problems. The algorithm has a new rule for updating the radius of the trust region. We establish the convergence of the improved $q$-trust region algorithm for solving unconstrained optimization problems under the conditions that the function is continuously $q$-differentiable and so on. Finally, numerical experiments show that our algorithm is effective. Compared with the improved $q$-trust region algorithm proposed by Zhou, our proposed improved $q$-trust region algorithm not only iterates to the optimal point faster, but also solves optimization problems with multiple optimal solutions. The results obtained in this paper extend and improve some existing results in the literature.

Key words: $q$-derivative, trust region algorithm, trust region radius, unconstrained optimization, continuous $q$-differentiability

中图分类号:

O224

仇英茗, 彭建文. 求解无约束优化问题的改进q-信赖域算法[J]. 运筹学学报（中英文）, 2026, 30(2): 209-224.

QIU Yingming, PENG Jianwen. Improved q-trust region algorithm for unconstrained optimization problems[J]. Operations Research Transactions, 2026, 30(2): 209-224.

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求解无约束优化问题的改进q-信赖域算法

Improved q-trust region algorithm for unconstrained optimization problems

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