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The paper contains second order necessary and sufficient conditions for a minimum, exact smooth penalty theorems and augmented Lagrangian duality theorems which cover the case when more than one collection of Lagrange multipliers exist and the second order quadratic function can be lower estimated only by norms weaker than that in which the cost function and constrained mappings are differentiable.
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A. D. Ioffe (1979) studied this question.
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