El teorema de Karush-Kuhn-Tucker, una generalización del teorema de los multiplicadores de Lagrange, y programación convexa

This paper expects to show a generalization of the Lagrange multiplier rule, which solves optimization problems with only equality constraints. The Karush-Kuhn-Tucker theorem is an extention of this result in which inequality constraints are also considered. In the first section of this text, we discuss the Lagrange multiplier rule, including one example. In the second one, we prove the Karush-Kuhn-Tucker theorem, including another example. In the third and last one, we make a brief introduction to convex and concave programming and we prove a sufficient condition in convex and concave programming.