Abstract
For nonsmooth infinite optimization problems with inequality constraints, nonasymptotic conditions of F. John and Karush-Kuhn-Tucker type in terms of approximate derivatives are established, the Lagrange multiplier being a nonnegative Radon measure on the index set which is assumed to be a compact Hausdorff space. The result is obtained with the aid of a Farkas type theorem for infinite systems of nonlinear inequalities.
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