Nonlinear perturbations for linear semi-infinite optimization problems

A perturbation method for solving semi-infinite optimization problems is introduced. The approach is to use the continuous structure of the problem rather than an a priori discretization of the constraint set. A duality theory for infinite-dimensional convex programs is used to construct a nonlinear dual problem which is a finite-dimensional unconstrained concave problem. This induced dual problem penalizes the classical semi-infinite problem. This formulation lends itself to computing a solution of the dual by Newton´s type method and allows for solving both the primal and dual problems. Implementation of a primal-dual algorithm, the connection with interior point methods, and further results are briefly discussed