Global Convergence of Algorithms with Nonmonotone Line Search Strategy in Unconstrained Optimization

Bjorn Huther

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Global Convergence of Algorithms with Nonmonotone Line Search Strategy in Unconstrained Optimization

机译：无约束优化中具有非单调线搜索策略的算法的全局收敛性

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摘要

In this paper we state some nonmonotone line search strategies for unconstrained optimization algorithms. Abstracting from the concrete line search strategy we prove two general convergence results. Using this theory we can show the global convergence of the BFGS method with nonmonotone line search strategy. In contrast to some former results about nonmonotone line search strategies, both our convergence results and their proofs are natural generalizations of known results for the monotone case.

机译：在本文中，我们针对无约束优化算法提出了一些非单调线搜索策略。从具体的线搜索策略中抽象出来，我们证明了两个一般的收敛结果。使用该理论，我们可以证明BFGS方法与非单调线搜索策略的全局收敛性。与以前有关非单调搜索策略的一些结果相反，我们的收敛结果及其证明都是单调情况下已知结果的自然概括。

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来源
《Results in mathematics》 |2002年第4期|共14页
作者
Bjorn Huther;
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正文语种 eng
中图分类数学;
关键词
Nonmonotone line search strategy; BFGS method; global convergence; AMS subject classification;

机译：非单调线搜索策略;BFGS方法;全局收敛;AMS主题分类;

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专利

1. Global Convergence of Algorithms with Nonmonotone Line Search Strategy in Unconstrained Optimization [J] . Bjorn Huther Results in mathematics . 2002,第3a4期

机译：无约束优化中具有非单调线搜索策略的算法的全局收敛性
2. Global Convergence of a Nonmonotone Trust Region Algorithm with Memory for Unconstrained Optimization [J] . Zhensheng Yu, Anqi Wang Journal of Mathematical Modelling and Algorithms . 2011,第2期

机译：带约束的带记忆的非单调信赖域算法的全局收敛性
3. Global Convergence of an Extended Descent Algorithm without Line Search for Unconstrained Optimization [J] . Cuiling Chen, Liling Luo, Caihong Han, Journal of Applied Mathematics and Physics . 2018,第1期

机译：无线搜索的无约束优化的扩展下降算法的全局收敛性
4. On the Global Convergence of Nonmonotone Trust Region Algorithms for Nonsmooth Optimization [C] . Xi Min, Zhou Houchun 2011 International Conference on Computer and Management . 2011

机译：非光滑优化的非单调信赖域算法的全局收敛性
5. Trust-search algorithms for unconstrained optimization. [D] . Kroyan, Julia. 2004

机译：用于无约束优化的信任搜索算法。
6. A modified nonmonotone BFGS algorithm for unconstrained optimization [O] . Xiangrong Li, Bopeng Wang, Wujie Hu -1

机译：改进的非单调BFGS算法无约束优化
7. A nonmonotone globalization algorithm with preconditioned gradient path for unconstrained optimization [O] . Zhou Q, Sun W, Qi L 2010

机译：无条件优化的带预处理梯度路径的非单调全球化算法

Global Convergence of Algorithms with Nonmonotone Line Search Strategy in Unconstrained Optimization

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