On Karush Kuhn Turker’s Theorem and the Lagrange Iterative Method of Solving Nonlinear Constrained..

The statement and proof of the Karush Kuhn Turker's theorem as a characterization of the behaviour of the objective and constraint functions at local optima of inequality constrained optimization problems, as well as the necessary and sufficient conditions for the Lagrangian method as a prerequisite for the convergence of the Lagrangian iterative method, are included in this work. As a result, it is presented as a solution that is more effective in addressing the restricted optimization issue. To begin, non-negativity constraints, if any, must be included in the m constraints, and if the unconstrained optimum of does not fulfil all constraints, the constrained optimum must occur at a solution space border point. For the Kahn-Tucker technique, this means that one constraint must be satisfied in equation form. This means that before the essential iteration of the Lagrangian technique can work in the maximising of concave functions or the minimization of convex functions, one constraint must be satisfied in equation form for the Kahn-Tucker approach to properly follow.

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