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An adaptive discretization method solving semi-infinite optimization problems with quadratic rate of convergence

: Seidel, T.; Küfer, K.-H.


Optimization (2020), Online First
ISSN: 0233-1934
ISSN: 0323-3898
Fraunhofer ITWM ()

Semi-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.] 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.