"Infeasibility Detection and SQP Methods for Nonlinear Optimization"
R. Byrd, F. Curtis, J. Nocedal
Technical Report, Optimization Center, Northwestern University (2008).

This paper addresses the need for nonlinear programming algorithms that provide fast local convergence guarantees no matter if a problem is feasible or infeasible. We present an active-set sequential quadratic programming method derived from an exact penalty approach that adjusts the penalty parameter appropriately to emphasize optimality over feasibility, or vice versa. Conditions are presented under which superlinear convergence is achieved in the infeasible case. Numerical experiments illustrate the practical behavior of the method.
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