Solving a Class of Variational Inequality Problems with a New Inexact Strategy

Xiaomei Dong (), Xingju Cai (), Deren Han () and Zhili Ge
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Xiaomei Dong: School of Mathematical Sciences, Key Laboratory for NSLSCS of Jiangsu Province, Nanjing Normal University, Nanjing 210023, P. R. China
Xingju Cai: School of Mathematical Sciences, Key Laboratory for NSLSCS of Jiangsu Province, Nanjing Normal University, Nanjing 210023, P. R. China
Deren Han: School of Mathematics and Systems Sciences, Beihang University, Beijing 100191, P. R. China
Zhili Ge: Department of Basic Sciences, Nanjing Polytechnic Institute, Nanjing 210048, P. R. China

Asia-Pacific Journal of Operational Research (APJOR), 2020, vol. 37, issue 01, 1-20

Abstract: We consider a class of variational inequality problems with linear constraints, where the mapping is unknown and the system is an oracle. The capacitated traffic congestion pricing problem of transportation is such an application, and many classical methods cannot deal with this class of problems. Note that the cost of the observation (observe the exact solution of the subproblem) is very expensive. It is important to get an inexact solution instead of an exact solution, especially when the iteration is far from the solution set. In this paper, we propose a modified inexact prediction–correction method. Under the mild condition that the underlying mapping is strongly monotone, we prove the global convergence. Some numerical examples are presented to illustrate the efficiency of the inexact strategy.

Keywords: Strongly monotone variational inequality problems; inexact strategy; linear constraints; traffic equilibrium (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1142/S0217595919500386

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