A feasible point adaptation of the Blankenship and Falk algorithm for semi‐infinite programming

Discretization methods for semi‐infinite programming do not provide a feasible point in a finite number of iterations. We propose a method that computes a feasible point with an objective value better than or equal to a target value f 0 or proves that such a point does not exist. Then a binary search on the space of objective values can be performed to obtain a feasible, ϵ ‐optimal solution. The algorithm is based on the algorithm proposed in (Blankenship and Falk, 1976). Under mild assumptions it terminates in a finite number of iterations.