An active set quasi-Newton method with projection step for monotone nonlinear equations

AIMS Mathematics

Peixin Li¹  Zhensheng Yu¹ 

[1] College of Science, University of Shanghai for Science and Technology, Shanghai, 200093, China;

关键词: constrained nonlinear equations;    active set;    quasi-newton;    global convergence;    projection;   

DOI  :  10.3934/math.2021215

来源: DOAJ

【 摘 要 】

In this paper, an active set quasi-Newton method for bound constrained nonlinear equation is proposed. By using this active set technique, we only need to solve a reduced dimension linear equation at each iteration to generate the search direction. The algorithm is a combination of the quasi-Newton method and projection method. Firstly we use the quasi-Newton step as the trial step and then use a projection technique to generate the next iteration point. Our key observation is that the algorithm generates a bounded iteration sequence automatically even if the bounds are equal to infinity and the global convergence is obtained in the sense that the whole sequence converges to the stationary point. The numerical tests show the efficiency of the algorithm.

【 授权许可】

Unknown