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We use sensitivity analysis to design $\textit{optimality-based}$discretization (cutting-plane) methods for the global optimization of nonconvexsemi-infinite programs (SIPs). We begin by formulating the optimaldiscretization of SIPs as a max-min problem and propose variants that are morecomputationally tractable. We then use parametric sensitivity theory to designan efficient method for solving these max-min problems to local optimality andargue this yields valid discretizations without sacrificing global optimalityguarantees. Finally, we formulate optimality-based $\textit{generalized}$discretization of SIPs as max-min problems and design efficient localoptimization algorithms to solve them approximately. Numerical experiments ontest instances from the literature demonstrate that our new optimality-baseddiscretization methods can significantly reduce the number of iterations forconvergence relative to the classical feasibility-based method.

Optimality-Based Discretization Methods for the Global Optimization of Nonconvex Semi-Infinite Programs