Some properties on quadratic infinite programs of integral type

In this work, we investigate the properties of a class of quadratic infinite programs where the objective is a quadratic functional of integral type and the feasible region is a subset of the infinite dimensional space Lp([0,1])Lp([0,1]). We first derive a dual problem of the primal problem to demonstrate that there is no duality gap between them. Then we prove that the objective function depends continuously on the design function. Two existence theorems for this kind of optimization problem are presented. These theoretical results may prove useful in the design of efficient algorithms for this class of infinite programming problem.