A Robust Algorithm for Optimization with General Equality and Inequality Constraints

Abstract

An algorithm for general nonlinearly constrained optimization is presented, which solves an unconstrained piecewise quadratic subproblem and a quadratic programming subproblem at each iterate. The algorithm is robust since it can circumvent the difficulties associated with the possible inconsistency of QP subproblem of the original SQP method. Moreover, the algorithm can converge to a point which satisfies a certain first-order necessary optimality condition even when the original problem is itself infeasible, which is a 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--Powell SQP algorithm at feasible points of the original problem. Under certain assumptions, it is shown that the algorithm coincides with the Han--Powell method when the iterates are sufficiently close to the solution. Some global convergence results are proved and locally superlinear convergence results are also obtained. Preliminary numerical results are reported.