新疆师范大学学报（自然科学版）2024，Vol.43Issue(4)：44-52,9.
一种非精确非光滑信赖域算法
An Inexact Trust Region Algorithm for Nonsmooth Optimization
摘要
Abstract
Aravkin et al proposed the trust region algorithm(employing exact gradients of f)for solving the nonsmooth optimization problem min x ∈ Rd f(x)+h(x),where f is a continuously differentiable function and h is a lower semicontinuous and prox-bounded proper function.In the case when f:=1n ∑n i=1 fi(n is quite big,and each component fi is continuously differentiable),the efficient algorithm for solving such kind of large-scale separable nonsmooth optimization problem is studied.Combining the concepts of the inexact algorithm and the above trust-region algorithm,it is proposed that the inexact trust-region algorithm replaces the exact gradients with the inexact gradients for solving this nonsmooth problem.Comparing with the trust-region algorithm(employing the exact gradients of f),the new algorithm can reduce the computational cost at each iteration.Under certain assumptions,the iteration complexity of this algorithm is established.关键词
大规模可分离非光滑优化/非精确信赖域算法/邻近梯度算法Key words
Large-scale separable nonsmooth optimization/Inexact trust-region algorithm/Proximal gradient method分类
数理科学引用本文复制引用
李祉赟,王湘美,马德乐..一种非精确非光滑信赖域算法[J].新疆师范大学学报（自然科学版）,2024,43(4):44-52,9.基金项目
国家自然科学基金项目(12161017) （12161017）
贵州省省级科技计划项目(ZK[2022]110). （ZK[2022]110）
