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

• Published in: Chinese annals of mathematics. Serie B Vol. 29; no. 3; pp. 273 - 290
• Main Authors: Wang, Yunjuan, Zhu, Detong
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 01.05.2008; Arts and Science School,Shanghai Dianji University,Shanghai 200240,China%Business College,Shanghai Normal University,Shanghai 200234,China; Mathematics and Science College,Shanghai Normal University,Shanghai 200234,China
• Subjects: Applications of Mathematics; Mathematics; Mathematics and Statistics; Trust region; Affine scaling; 90C33; Variational inequality problem; Optimal path; Interior point; 49M99
• ISSN: 0252-9599; 1860-6261
• DOI: 10.1007/s11401-007-0082-6

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.