A robust algorithm or optimization with general equality and inequality constraints

An algorithm for general nonlinearly constrained optimization is presented, which solves an unconstrained piecewise quadratic subproblem and quadratic programming subproblem at each iterate. The algorithm is robust since it c an circumvent the difficulties associated with the possible inconsistency o f QP subproblem of the original SQP method. Moreover, the algorithm can con verge to point which satis es certain first-order necessary optimality cond ition even when the original problem is itself infeasible, which is feature of Burke and Han's methods [ Math. Programming, 43 ( 1989), pp. 277-303]. Unlike Burke and Han's methods, our algorithm does not introduce additional bound constraints. The algorithm solves the same subproblems as the Han Po well SQP algorithm at feasible points of the original problem. Under certai n assumptions, it is shown that the algorithm coincides with the Han-Powell method when the iterates are sufficiently close to the solution. Some glob al convergence results are proved and locally superlinear convergence resul ts are also obtained. Preliminary numerical results are reported.