In this paper, we consider a finite-dimensional optimization problem minimizing a continuous objective on a compact domain subject to a multi-dimensional constraint function. For the latter, we assume the availability of a global Lipschitz constant. In recent literature, methods based on...

Spatial branch-and-bound algorithms for global minimization of non-convex problems require both lower and upper bounding procedures that finally converge to a globally optimal value in order to ensure termination of these methods. Whereas convergence of lower bounds is commonly guaranteed for...

We present a branch-and-bound algorithm for globally solving parabolic optimal control problems with binary switches that have bounded variation and possibly need to satisfy further combinatorial constraints. More precisely, for a given tolerance ε0, we show how to compute in finite time an...

Existing algorithms for generalized semi-infinite programs can only handle lower-level constraints containing equality constraints depending on upper-level variables (so-called coupling equality constraints) under limiting assumptions. More specifically, discretization-based algorithms require...