  We use sensitivity analysis to design $\textit{optimality-based}$
discretization (cutting-plane) methods for the global optimization of nonconvex
semi-infinite programs (SIPs). We begin by formulating the optimal
discretization of SIPs as a max-min problem and propose variants that are more
computationally tractable. We then use parametric sensitivity theory to design
an efficient method for solving these max-min problems to local optimality and
argue this yields valid discretizations without sacrificing global optimality
guarantees. Finally, we formulate optimality-based $\textit{generalized}$
discretization of SIPs as max-min problems and design efficient local
optimization algorithms to solve them approximately. Numerical experiments on
test instances from the literature demonstrate that our new optimality-based
discretization methods can significantly reduce the number of iterations for
convergence relative to the classical feasibility-based method.
