An Accelerated Three-Term Conjugate Gradient Method with Sufficient Descent Condition and Conjugacy Condition

XiaoLiang Dong (), Deren Han (), Zhifeng Dai (), Lixiang Li () and Jianguang Zhu ()
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XiaoLiang Dong: North Minzu University
Deren Han: Beihang University
Zhifeng Dai: Changsha University of Science and Technology
Lixiang Li: Guilin University of Electronic Technology
Jianguang Zhu: Shandong University of Science and Technology

Journal of Optimization Theory and Applications, 2018, vol. 179, issue 3, No 10, 944-961

Abstract: Abstract An accelerated three-term conjugate gradient method is proposed, in which the search direction can satisfy the sufficient descent condition as well as extended Dai–Liao conjugacy condition. Different from the existent methods, a dynamical compensation strategy in our proposed method is considered, that is Li–Fushikuma-type quasi-Newton equation is satisfied as much as possible, otherwise, to some extent, the singular values of iteration matrix of search directions will adaptively clustered, which substantially benefits acceleration the convergence or reduction in the condition number of iteration matrix. Global convergence is established under mild conditions for general objective functions. We also report some numerical results to show its efficiency.

Keywords: Three-term conjugate gradient method; Sufficient descent condition; Conjugacy condition; Global convergence; Condition number; 90C30 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10957-018-1377-3

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