A hybrid LQP-based method for structured variational inequalities

Abstract

This paper proposes a hybrid LQP-based method (LQP, logarithmic-quadratic proximal) to solve a class of structured variational inequalities. In this method, an intermediate point is produced by solving a nonlinear equation system based on the LQP method; a descent direction is constructed using this iterate and the new iterate is obtained by a convex combination of the previous point and the one generated by a projection-type method along this descent direction. Global convergence of the new method is proved under mild assumptions. Preliminary numerical results for traffic equilibrium problems verify the computational preferences of the new method.

Keywords:

• structured variational inequality
• logarithmic-quadratic proximal
• alternating direction method
• projection
• descent direction

2000 AMS Subject Classifications :

• 47J20
• 90C25
• 90C30

Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant No. 11001053) and the Research Award Fund for Outstanding Young Teachers in Southeast University.