We consider inference in weakly identified moment condition models when additional partially identifying moment inequality constraints are available. We detail the limiting distribution of the estimation criterion function and consequently propose a confidence set estimator for the true parameter.National Science Foundation of China (Grant ID: 71301026)This is the author accepted manuscript. The final version is available from Elsevier via http://dx.doi.org/10.1016/j.spl.2016.06.01