Abstract
An alternate form of the Karush–Kuhn–Tucker (KKT) first-order optimality conditions is described where the inequality constraints are not converted to the equality form by introduction of the slack variables. The requirement of “regular points” in the KKT conditions is examined and explained. Second-order necessary and sufficient conditions for the constrained optimization problem are presented, explained, and illustrated. The concept of duality in nonlinear programming is introduced and explained. The dual function is defined and the Lagrangian duality is discussed for an equality-constrained problem. It is then extended for inequality constraints as well. The concept of saddle points is introduced, and the saddle point theorem is discussed.
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