A novel sphere packing problem is introduced. A maximum number of spheres of different radii should be placed such that the spheres do not overlap and their centers fulfill a quasi-containment condition. The latter allows the spheres to lie partially outside the given cuboidal container....

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...

We present a novel relaxation for general nonconvex sparse MINLP problems, called overlapping convex hull relaxation (CHR). It is defined by replacing all nonlinear constraint sets by their convex hulls. If the convex hulls are disjunctive, e.g. if the MINLP is block-separable, the CHR is...

Computing a sample mean of time series under dynamic time warping is NP-hard. Consequently, there is an ongoing research effort to devise efficient heuristics. The majority of heuristics have been developed for the constrained sample mean problem that assumes a solution of predefined length. In...

A bundle method for minimizing the difference of convex (DC) and possibly nonsmooth functions is developed. The method may be viewed as an inexact version of the DC algorithm, where each subproblem is solved only approximately by a bundle method. We always terminate the bundle method after the...

In this paper, a new method for computing an enclosure of the nondominated set of multiobjective mixed-integer quadratically constrained programs without any convexity requirements is presented. In fact, our criterion space method makes use of piecewise linear relaxations in order to bypass the...

The minimum sum-of-squares clustering problem is a very important problem in data mining and machine learning with very many applications in, e.g., medicine or social sciences. However, it is known to be NP-hard in all relevant cases and to be notoriously hard to be solved to global optimality...

This article investigates the approximation quality achievable for biobjective minimization problems with respect to the Pareto cone by solutions that are (approximately) optimal with respect to larger ordering cones. When simultaneously considering α-approximations for all closed convex...

Recently, Bomze et al. introduced a sparse conic relaxation of the scenario problem of a two stage stochastic version of the standard quadratic optimization problem. When compared numerically to Burer's classical reformulation, the authors showed that there seems to be almost no difference in...

For over 10 years, the constraint integer programming framework SCIP has been extended by capabilities for the solution of convex and nonconvex mixed-integer nonlinear programs (MINLPs). With the recently published version 8.0, these capabilities have been largely reworked and extended. This...