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An affine scaling interior trust region method via optimal path for solving monotone variational inequality problem with linear constraints

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Abstract

Based on a differentiable merit function proposed by Taji et al. in “Math. Prog. Stud., 58, 1993, 369–383”, the authors propose an affine scaling interior trust region strategy via optimal path to modify Newton method for the strictly monotone variational inequality problem subject to linear equality and inequality constraints. By using the eigensystem decomposition and affine scaling mapping, the authors from an affine scaling optimal curvilinear path very easily in order to approximately solve the trust region subproblem. Theoretical analysis is given which shows that the proposed algorithm is globally convergent and has a local quadratic convergence rate under some reasonable conditions.

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Authors and Affiliations

  1. Mathematics and Science College, Shanghai Normal University, Shanghai, 200234, China

    Yunjuan Wang

  2. Business College, Shanghai Normal University, Shanghai, 200234, China

    Detong Zhu

  3. Arts and Science School, Shanghai Dianji University, Shanghai, 200240, China

    Yunjuan Wang

Authors
  1. Yunjuan Wang
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  2. Detong Zhu
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Corresponding author

Correspondence to Yunjuan Wang.

Additional information

Project supported by the National Natural Science Foundation of China (No. 10471094), the Doctoral Programmer Foundation of the Ministry of Education of China (No. 0527003), the Shanghai Leading Academic Discipline Project (No. T0401), and the Science Foundation Grant of Shanghai Municipal Education Committee (Nos. 05DZ11, 06A110).

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Wang, Y., Zhu, D. An affine scaling interior trust region method via optimal path for solving monotone variational inequality problem with linear constraints. Chin. Ann. Math. Ser. B 29, 273–290 (2008). https://doi.org/10.1007/s11401-007-0082-6

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  • DOI: https://doi.org/10.1007/s11401-007-0082-6

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