A reduced Hessian SQP method for inequality constrained optimization

This paper develops a reduced Hessian method for solving inequality constrained optimization problems. At each iteration, the proposed method solves a quadratic subproblem which is always feasible by introducing a slack variable to generate a search direction and then computes the steplength by adopting a standard line search along the direction through employing the l ∞ penalty function. And a new update criterion is proposed to generate the quasi‐Newton matrices, whose dimensions may be variable, approximating the reduced Hessian of the Lagrangian. The global convergence is established under mild conditions. Moreover, local R‐linear and superlinear convergence are shown under certain conditions.