Lawrence, Craig T.Tits, A.L.A sequential Quadratic Programming algorithm designed to efficiently solve nonlinear optimization problems with many inequality constraints, e.g. problems arising from finely discretized Semi-Infinite Programming, is described and analyzed. The key features of the algorithm are (i) that only a few of the constraints are used in the QP sub-problems at each iteration, and (ii) that every iterate satisfies all constraints.en-USoptimal controloptimizationIntelligent Control SystemsTechnical Report