Global and superlinear convergence of inexact sequential quadratically constrained quadratic programming method for convex programming

This paper is concerned with a sequential quadratically constrained quadratic programming (SQCQP) method for convex programming. The SQCQP method solves, at each iteration, a quadratically constrained quadratic programming subproblem whose objective function and constraints are quadratic approximations to the objective function and constraints of the original problem, respectively. We propose an inexact SQCQP method which solves inexactly the subproblem and prove its global and superlinear convergence properties.