The classical Fritz John conditions have been enhanced through the addition of an extra necessary condition, and their effectiveness has been significantly improved (for the case where X is a closed convex set, and Bertsekas and Ozdaglar [1] for the case where X is a closed set). In this paper we will use the following assumptions instead of smoothness and the assumption of existence of an optimal solution will retain.

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Fritz John Conditions Lower Semicontinuous Functions Convex Programming Problem