A Robust Algorithm for Optimization with General Equality and Inequality Constraints

An algorithm for general nonlinearly constrained optimization is presented, which solves an unconstrained piecewise quadratic subprob-lem and a quadratic programming subproblem at each iterate. The algorithm is robust since it can circumvent the diiculties associated with the possible inconsistency of QP subproblem of the original SQP method. Moreover, the algorithm can converge to a point which satis-es a certain rst-order necessary optimality condition even when the original problem is itself infeasible, which is a feature of Burke and Han's methods(1989). Unlike Burke and Han's methods(1989), however , we do not introduce additional bound constraints. The algorithm solves the same subproblems as Han-Powell SQP algorithm at feasible points of the original problem. Under certain assumptions, it is shown that the algorithm coincide with the Han-Powell method when the iterates are suuciently close to the solution. Some global convergence results are proved and local superlinear convergence results are also obtained. Preliminary numerical results are reported.