On the rate of convergence of sequential quadratic programming with nondifferentiable exact penalty function in the presence of constraint degeneracy

On the rate of convergence of sequential quadratic programming with nondifferentiable exact penalty function in the presence of constraint degeneracy

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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:
Keywords: penalty functions
Abstract:

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.

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