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...

We propose a multi-swarm approach to approximate the Pareto front of general multi-objective optimization problems that is based on the consensus-based optimization method (CBO). The algorithm is motivated step by step beginning with a simple extension of CBO based on fixed scalarization...

In this article, we consider distance-based clustering problems. In contrast to many approaches, we use the maximum norm instead of the more commonly used Euclidean norm to measure distances. This problem is nonsmooth and non-convex and, thus, difficult to solve to global optimality using...