2 citations · 8 across the 13 of their papers we have counts for
13 papers
A Solution Concept for Convex Vector Optimization Problems based on a User-defined Region of Interest
Daniel Dörfler, Rebecca Köhler, Andreas Löhne
This work addresses arbitrary convex vector optimization problems, which constitute a general framework for multi-criteria decision-making in diverse real-world applications. Due t…
MOCVXPY: a CVXPY extension for multiobjective optimization
Ludovic Salomon, Daniel Dörfler, Andreas Löhne
MOCVXPY is an open-source Python library for convex vector optimization. It is built on top of CVXPY, a domain-specific language for single-objective convex optimization. MOCVXPY e…
Computing all Nash equilibria of low-rank bi-matrix games
Zachary Feinstein, Andreas Löhne, Birgit Rudloff
We study constrained bi-matrix games, with a particular focus on low-rank games. Our main contribution is a framework that reduces low-rank games to smaller, equivalent constrained…
Low-Rank Multi-Objective Linear Programming
Andreas Löhne, Pascal Zillmann
When solving multi-objective programs (MOLPs), the number of objectives essentially determines the computing time. This can even lead to practically unsolvable problems. Consequent…
A Decision-Making Method in Polyhedral Convex Set Optimization
Andreas Löhne
Optimization problems with set-valued objective functions arise in contexts such as multi-stage optimization with vector-valued objectives. The aim is to identify an optimizer -- a…
Multi-objective stochastic linear programming with recourse and flexible decision making
Andreas H. Hamel, Andreas Löhne
Optimal inventory leads to stochastic optimization problems where deterministic delivery decisions have to be made in advance of stochastic demand realizations. Similarly, risk dep…
Convex sets approximable as the sum of a compact set and a cone
Daniel Dörfler, Andreas Löhne
The class of convex sets that admit approximations as Minkowski sum of a compact convex set and a closed convex cone in the Hausdorff distance is introduced. These sets are called…
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 polyhedral approximation algorithm for recession cones of spectrahedral shadows
Daniel Dörfler, Andreas Löhne
The intersection of an affine subspace with the cone of positive semidefinite matrices is called a spectrahedron. An orthogonal projection thereof is called a spectrahedral shadow…
On unbounded polyhedral convex set optimization problems
Niklas Hey, Andreas Löhne
A polyhedral convex set optimization problem is given by a set-valued objective mapping from the -dimensional to the -dimensional Euclidean space whose graph is a convex poly…
On the approximation error for approximating convex bodies using multiobjective optimization
Andreas Löhne, Fangyuan Zhao, Lizhen Shao
A polyhedral approximation of a convex body can be calculated by solving approximately an associated multiobjective convex program (MOCP). An MOCP can be solved approximately by Be…
Geometric duality and parametric duality for multiple objective linear programs are equivalent
Daniel Dörfler, Andreas Löhne
In 2011, Luc introduced parametric duality for multiple objective linear programs. He showed that geometric duality, introduced in 2008 by Heyde and Löhne, is a consequence of para…
Projection of polyhedral cones and linear vector optimization
Andreas Löhne
Consider a polyhedral convex cone which is given by a finite number of linear inequalities. We investigate the problem to project this cone into a subspace and show that this probl…