As for variational inequality problems, we define the optimal value function of trust region subproblems, study the properties of it. And then under strongly monotonic conditions, we use the optimal value function to provide a global error estimate for the feasible solution .
Zhao, Wenling and Huang, Jin
"A Global Error bound for the Feasible Solution of Variational Inequality Problems,"
Applied Mathematics & Information Sciences: Vol. 06
, Article 12.
Available at: https://dc.naturalspublishing.com/amis/vol06/iss3/12