Implicit function theorems and lagrange multipliers

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Abstract
Several implicit function theorems are proved, for systems of inequalities as well as equalities, assuming weaker differentiability than continuous Fréchet. These results give sufficient hypotheses for the Kuhn-Tucker conditions to hold, in a constrained minimization problem, with cone constraints and in any dimension. A condition is given for an inequality constraint system to be equivalently replaced by another, for which the function involved has surjective derivative. This allows some known implicit function theorems to be applied to inequality systems.