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Necessary optimality conditions for nonlinear programming are discussed in the present research. A new second-order condition is given, which depends on a weak constant rank constraint requirement. We show that practical and publicly available algorithms (www.ime.usp.br/∼egbirgin/tango) of augmented Lagrangian type converge, after slight modifications, to stationary points defined by the new condition.
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Andreani et al. (2007) studied this question.
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