In this article, we introduce the rectangular knapsack problem as a special case of the quadratic knapsack problem consisting in the maximization of the product of two separate knapsack profits subject to a cardinality constraint. We propose a polynomial time algorithm for this problem that...

While branch and bound based algorithms are a standard approach to solve single-objective (mixed-)integer optimization problems, multi-objective branch and bound methods are only rarely applied compared to the predominant objective space methods. In this paper we propose modifications to...

Algorithms generating piecewise linear approximations of the nondominated set for general, convex and nonconvex, multicriteria programs are developed. Polyhedral distance functions are used to construct the approximation and evaluate its quality. The functions automatically adapt to the problem...

The problem of optimizing a biconvex function over a given (bi)convex or compact set frequently occurs in theory as well as in industrial applications, for example, in the field of multifacility location or medical image registration. Thereby, a function <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$f:X\times Y\to{\mathbb{R}}$$</EquationSource> </InlineEquation> is...</equationsource></inlineequation>

In the last years a multitude of algorithms have been proposed to solve multiobjective integer programming problems. However, only few authors offer open-source implementations. On the other hand, new methods are typically compared to code that is publicly available, even if this code is known...