Infinite programming and theorems of the alternative - Montiel López, Pablo; Ruiz Galán, Manuel (Mathematical methods in the applied sciences, 2019)
In this paper, we obtain optimal versions of the Karush–Kuhn–Tucker, Lagrange multiplier, and Fritz John theorems for a nonlinear infinite programming problem where both the number of equality and inequality constraints is arbitrary. To this end, we make use of a theorem of the alternative for a family of functions satisfying a certain type of weak convexity, the so‐called infsup‐convexity.