84 citations · 422 across the 20 of their papers we have counts for
21 papers
A solution method for arbitrary polyhedral convex set optimization problems
Andreas Löhne
We provide a solution method for the polyhedral convex set optimization problem, that is, the problem to minimize a set-valued mapping with polyhedral convex graph with respect to…
The natural ordering cone of a polyhedral convex set-valued objective mapping
Andreas Löhne
For a given polyhedral convex set-valued mapping we define a polyhedral convex cone which we call the natural ordering cone. We show that the solution behavior of a polyhedral conv…
Existence of solutions for polyhedral convex set optimization problems
Andreas Löhne
Polyhedral convex set optimization problems are the simplest optimization problems with set-valued objective function. Their role in set optimization is comparable to the role of l…
Approximate Vertex Enumeration
Andreas Löhne
The problem to compute the vertices of a polytope given by affine inequalities is called vertex enumeration. The inverse problem, which is equivalent by polarity, is called the con…
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…
Solving polyhedral d.c. optimization problems via concave minimization
Simeon vom Dahl, Andreas Löhne
The problem of minimizing the difference of two convex functions is called polyhedral d.c. optimization problem if at least one of the two component functions is polyhedral. We cha…
Computing Convex Hulls of Trajectories
Daniel Ciripoi, Nidhi Kaihnsa, Andreas Löhne +1
We study the convex hulls of trajectories of polynomial dynamical systems. Such trajectories include real algebraic curves. The boundaries of the resulting convex bodies are strati…
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…
A set optimization approach to zero-sum matrix games with multi-dimensional payoffs
Andreas H. Hamel, Andreas Loehne
A new solution concept for two-player zero-sum matrix games with multi-dimensional payoff is introduced. It is based on extensions of vector orders in K-dimensional spaces to order…
Solving DC programs with a polyhedral component utilizing a multiple objective linear programming solver
Andreas Löhne, Andrea Wagner
A class of non-convex optimization problems with DC objective function is studied, where DC stands for being representable as the difference of two convex functions and…
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…
Set optimization - a rather short introduction
Andreas H. Hamel, Frank Heyde, Andreas Löhne +2
Recent developments in set optimization are surveyed and extended including various set relations as well as fundamental constructions of a convex analysis for set- and vector-valu…
On the Dual of the Solvency Cone
Andreas Löhne, Birgit Rudloff
A solvency cone is a polyhedral convex cone which is used in Mathematical Finance to model proportional transaction costs. It consists of those portfolios which can be traded into…
Primal and Dual Approximation Algorithms for Convex Vector Optimization Problems
Andreas Löhne, Birgit Rudloff, Firdevs Ulus
Two approximation algorithms for solving convex vector optimization problems (CVOPs) are provided. Both algorithms solve the CVOP and its geometric dual problem simultaneously. The…
Benson type algorithms for linear vector optimization and applications
Andreas H. Hamel, Andreas Löhne, Birgit Rudloff
New versions and extensions of Benson's outer approximation algorithm for solving linear vector optimization problems are presented. Primal and dual variants are provided in which…
Lagrange duality, stability and subdifferentials in vector optimization
Elvira Hernández, Andreas Löhne, Luis Rodríguez-Marín +1
Langrange duality theorems for vector and set optimization problems which are based on an consequent usage of infimum and supremum (in the sense greatest lower and least upper boun…
An Algorithm to Solve Polyhedral Convex Set Optimization Problems
Andreas Löhne, Carola Schrage
An algorithm which computes a solution of a set optimization problem is provided. The graph of the objective map is assumed to be given by finitely many linear inequalities. A solu…
Lagrange Duality in Set Optimization
Andreas H. Hamel, Andreas Löhne
Based on the complete-lattice approach, a new Lagrangian duality theory for set-valued optimization problems is presented. In contrast to previous approaches, set-valued versions f…
An algorithm for calculating the set of superhedging portfolios in markets with transaction costs
Andreas Löhne, Birgit Rudloff
We study the explicit calculation of the set of superhedging portfolios of contingent claims in a discrete-time market model for d assets with proportional transaction costs. The s…