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

Abstract

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

CLC Number:

O224

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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Improved q-trust region algorithm for unconstrained optimization problems

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