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Global convergence of an SQP algorithm for nonlinear optimization with overdetermined constraints

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  • A sequential quadratic programming (SQP) algorithm is presented for solving nonlinear optimization with overdetermined constraints. In each iteration, the quadratic programming (QP) subproblem is always feasible even if the gradients of constraints are always linearly dependent and the overdetermined constraints may be inconsistent. The $\ell_2$ exact penalty function is selected as the merit function. Under suitable assumptions on gradients of constraints, we prove that the algorithm will terminate at an approximate KKT point of the problem, or there is a limit point which is either a point satisfying the overdetermined system of equations or a stationary point for minimizing the $\ell_2$ norm of the residual of the overdetermined system of equations.
    Mathematics Subject Classification: Primary: 90C30, 90C51; Secondary: 65K05.


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