# American Institute of Mathematical Sciences

April  2014, 10(2): 461-476. doi: 10.3934/jimo.2014.10.461

## A new parallel splitting descent method for structured variational inequalities

 1 School of Mathematical Sciences, Jiangsu Key Laboratory for NSLSCS, Nanjing Normal University, Nanjing 210023, China, China 2 School of Mathematical Sciences, Jiangsu Key Labratory for NSLSCS, Nanjing Normal University, Nanjing, 210023

Received  October 2012 Revised  August 2013 Published  October 2013

In this paper, we propose a new parallel splitting descent method for solving a class of variational inequalities with separable structure. The new method can be applied to solve convex optimization problems in which the objective function is separable with three operators and the constraint is linear. In the framework of the new algorithm, we adopt a new descent strategy by combining two descent directions and resolve the descent direction which is different from the methods in He (Comput. Optim. Appl., 2009, 42: 195-212.) and Wang et al. (submitted to J. Optimiz. Theory App.). Theoretically, we establish the global convergence of the new method under mild assumptions. In addition, we apply the new method to solve problems in management science and traffic equilibrium problem. Numerical results indicate that the new method is efficient and reliable.
Citation: Kai Wang, Lingling Xu, Deren Han. A new parallel splitting descent method for structured variational inequalities. Journal of Industrial & Management Optimization, 2014, 10 (2) : 461-476. doi: 10.3934/jimo.2014.10.461
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