Seidel, TobiasTobiasSeidelKüfer, Karl-HeinzKarl-HeinzKüfer2022-03-062022-03-062022https://publica.fraunhofer.de/handle/publica/26594810.1080/02331934.2020.1804566Semi-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 [Infinitely constrained optimization problems. J Opt Theory Appl. 1976;19(2):261-281. https://doi.org/10.1007/BF00934096] 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.en003510006519journal article