An adaptive discretization method solving semi-infinite optimization problems with quadratic rate of convergence

Semi-infinite programming can be used to model a large variety of complex optimization problems. The simple description of such problems comes at a price: semi-infinite problems are often harder to solve than finite nonlinear problems. In this paper we combine a classical adaptive discretization method developed by Blankenship and Falk and techniques regarding a semi-infinite optimization problem as a bi-level optimization problem. We develop a new adaptive discretization method which combines the advantages of both techniques and exhibits a quadratic rate of convergence. We further show that a limit of the iterates is a stationary point, if the iterates are stationary points of the approximate problems

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 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, E-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