Article ID: | iaor20031203 |
Country: | Germany |
Volume: | 92 |
Issue: | 2 |
Start Page Number: | 359 |
End Page Number: | 386 |
Publication Date: | Jan 2002 |
Journal: | Mathematical Programming |
Authors: | Anitescu M. |
Keywords: | penalty functions |
We analyze the convergence of a sequential quadratic programming (SQP) method for nonlinear programming for the case in which the Jacobian of the active constraints is rank deficient at the solution and/or strict complementarity does not hold for some or any feasible Lagrange multipliers. We use a nondifferentiable exact penalty function, and we prove that the sequence generated by an SQP using a line search is locally R-linearly convergent if the matrix of the quadratic program is positive definite and constant over iterations, provided that the Mangasarian–Fromovitz constraint qualification and some second-order sufficiency conditions hold.