A globally convergent algorithm with adaptively refined discretization for semi-infinite optimization problems arising in engineering design

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Abstract
Although most of the algorithms that have been proposed for the solution of semi-infinite optimization problems make use, at each iteration, of a set of local maximizers over the range of the independent parameter, the question of suitably approximating such maximizers is generally left aside. It has been suggested that this issue can be addressed by means of an adaptively refined discretization of the interval of variation of the independent parameter. The algorithm proposed in the paper makes use of such a technique and, by means of a certain memory mechanism, avoids the potential lack of convergence suffered by an existing algorithm, while requiring a relatively small number of gradient evaluations.