A dual parameterization approach to linear–quadratic semi-infinite programming problems

Semi-infinite programming problems are special optimization problems in which a cost is to be minimized subject to infinitely many constraints. This class of problems has many real-world applications. In this paper, we consider a class of linear–quadratic semi-infinite programming problems. Using the duality theory, the dual problem is obtained, where the decision variables are measures. A new parameterization scheme is developed for approximating these measures. On this basis, an efficient algorithm for computing the solution of the dual problem is obtained. Rigorous convergence results are given to support the algorithm. The solution of the primal problem is easily obtained from that of the dual problem. For illustration, three numerical examples are included.