On the number of inner iterations per outer iteration of a globally convergent algorithm for optimization with general nonlinear inequality constraints and simple bounds A.R. Conn, Nick Gould and Ph.L. Toint Report 92/14 This paper considers the number of inner iterations required per outer iteration for the algorithm proposed by Conn, Gould and Toint in 1992. We show that asymptotically, under suitable reasonable assumptions, a single inner iteration suffices.