A globally convergent SQP method for semi-infinite nonlinear optimization
Journal of Computational and Applied Mathematics
Numerical experiments in semi-infinite programming
Computational Optimization and Applications
Evaluating derivatives: principles and techniques of algorithmic differentiation
Evaluating derivatives: principles and techniques of algorithmic differentiation
Interval analysis: theory and applications
Journal of Computational and Applied Mathematics - Special issue on numerical analysis in the 20th century vol. 1: approximation theory
Global Optimization of Nonlinear Bilevel Programming Problems
Journal of Global Optimization
Methods and Applications of Interval Analysis (SIAM Studies in Applied and Numerical Mathematics) (Siam Studies in Applied Mathematics, 2.)
Global solution of bilevel programs with a nonconvex inner program
Journal of Global Optimization
A review of recent advances in global optimization
Journal of Global Optimization
Towards global bilevel dynamic optimization
Journal of Global Optimization
Convergence rate of McCormick relaxations
Journal of Global Optimization
Computational Optimization and Applications
A lifting method for generalized semi-infinite programs based on lower level Wolfe duality
Computational Optimization and Applications
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A new approach for the numerical solution of smooth, nonlinear semi-infinite programs whose feasible set contains a nonempty interior is presented. Interval analysis methods are used to construct finite nonlinear, or mixed-integer nonlinear, reformulations of the original semi-infinite program under relatively mild assumptions on the problem structure. In certain cases the finite reformulation is exact and can be solved directly for the global minimum of the semi-infinite program (SIP). In the general case, this reformulation is over-constrained relative to the SIP, such that solving it yields a guaranteed feasible upper bound to the SIP solution. This upper bound can then be refined using a subdivision procedure which is shown to converge to the true SIP solution with finite ε-optimality. In particular, the method is shown to converge for SIPs which do not satisfy regularity assumptions required by reduction-based methods, and for which certain points in the feasible set are subject to an infinite number of active constraints. Numerical results are presented for a number of problems in the SIP literature. The solutions obtained are compared to those identified by reduction-based methods, the relative performances of the nonlinear and mixed-integer nonlinear formulations are studied, and the use of different inclusion functions in the finite reformulation is investigated.