Frontiers of Mathematics in China

, Volume 13, Issue 6, pp 1325–1340 | Cite as

Prediction-correction method with BB step sizes

  • Xiaomei Dong
  • Xingju Cai
  • Deren Han
Research Article


In the prediction-correction method for variational inequality (VI) problems, the step size selection plays an important role for its performance. In this paper, we employ the Barzilai-Borwein (BB) strategy in the prediction step, which is efficient for many optimization problems from a computational point of view. To guarantee the convergence, we adopt the line search technique, and relax the conditions to accept the BB step sizes as large as possible. In the correction step, we utilize a longer step length to calculate the next iteration point. Finally, we present some preliminary numerical results to show the efficiency of the algorithms.


BB step sizes projection method prediction-correction method line search 


65K05 90C30 90C33 


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The second author was supported in part by the National Natural Science Foundation of China (Grant Nos. 11871279, 11571178), and the third author was supported in part by the National Natural Science Foundation of China (Grant Nos. 11625105, 11431002).


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© Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Jiangsu Key Laboratory for NSLSCS, School of Mathematical SciencesNanjing Normal UniversityNanjingChina
  2. 2.School of Mathematics and Systems ScienceBeihang UniversityBeijingChina

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