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 f0 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, -optimal solution. The algorithm is based on the algorithm proposed in (Blankenship JW, Falk JE in J Optim Theory Appl 19(2):261–281, 1976). Under mild assumptions it terminates in a finite number of iterations.

Optimization Letters
Department of Technology and Operations Management

Tsoukalas, A.T. (2011). A Feasible Point Adaptation of the Blankenship and Falk Algorithm for Semi- Infinite Programming. Optimization Letters, 5, 705–716. Retrieved from http://hdl.handle.net/1765/134155