2 citations · 3 across the 2 of their papers we have counts for
6 papers
Finite Representation of Quantile Sets for Multivariate Data via Vector Linear Programming
Andreas Löhne, Benjamin Weißing
Empirical quantiles for finitely distributed univariate random variables can be obtained by solving a certain linear program. It is shown in this short note that multivariate empir…
A Benson-Type Algorithm for Bounded Convex Vector Optimization Problems with Vertex Selection
Daniel Dörfler, Andreas Löhne, Christopher Schneider +1
We present an algorithm for approximately solving bounded convex vector optimization problems. The algorithm provides both an outer and an inner polyhedral approximation of the upp…
Calculus of convex polyhedra and polyhedral convex functions by utilizing a multiple objective linear programming solver
Daniel Ciripoi, Andreas Löhne, Benjamin Weißing
The article deals with operations defined on convex polyhedra or polyhedral convex functions. Given two convex polyhedra, operations like Minkowski sum, intersection and closed con…
A vector linear programming approach for certain global optimization problems
Daniel Ciripoi, Andreas Löhne, Benjamin Weißing
Global optimization problems with a quasi-concave objective function and linear constraints are studied. We point out that various other classes of global optimization problems can…
The vector linear program solver Bensolve -- notes on theoretical background
Andreas Löhne, Benjamin Weißing
Bensolve is an open source implementation of Benson's algorithm and its dual variant. Both algorithms compute primal and dual solutions of vector linear programs (VLP), which inclu…
Equivalence between polyhedral projection, multiple objective linear programming and vector linear programming
Andreas Löhne, Benjamin Weißing
Let a polyhedral convex set be given by a finite number of linear inequalities and consider the problem to project this set onto a subspace. This problem, called polyhedral project…