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9 papers · 1 filter

math.OC2022★ 3 cited

Deep Learning the Efficient Frontier of Convex Vector Optimization Problems

Zachary Feinstein, Birgit Rudloff

In this paper, we design a neural network architecture to approximate the weakly efficient frontier of convex vector optimization problems (CVOP) satisfying Slater's condition. The…

math.OC2021★ 1 cited

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…

math.OC2021★ 1 cited

Characterizing and Computing the Set of Nash Equilibria via Vector Optimization

Zachary Feinstein, Birgit Rudloff

Nash equilibria and Pareto optimality are two distinct concepts when dealing with multiple criteria. It is well known that the two concepts do not coincide. However, in this work w…

math.OC2021

A LP relaxation based matheuristic for multi-objective integer programming

Duleabom An, Sophie N. Parragh, Markus Sinnl +1

Motivated by their success in the single-objective domain, we propose a very simple linear programming-based matheuristic for tri-objective binary integer programming. To tackle th…

math.OC2020★ 6 cited

Dynamic Set Values for Nonzero Sum Games with Multiple Equilibriums

Zachary Feinstein, Birgit Rudloff, Jianfeng Zhang

Nonzero sum games typically have multiple Nash equilibriums (or no equilibrium), and unlike the zero sum case, they may have different values at different equilibriums. Instead of…

math.OC2019★ 11 cited

Certainty Equivalent and Utility Indifference Pricing for Incomplete Preferences via Convex Vector Optimization

Birgit Rudloff, Firdevs Ulus

For incomplete preference relations that are represented by multiple priors and/or multiple -- possibly multivariate -- utility functions, we define a certainty equivalent as well…

math.OC2016★ 6 cited

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…

math.OC2015★ 26 cited

A Parametric Simplex Algorithm for Linear Vector Optimization Problems

Birgit Rudloff, Firdevs Ulus, Robert Vanderbei

In this paper, a parametric simplex algorithm for solving linear vector optimization problems (LVOPs) is presented. This algorithm can be seen as a variant of the multi-objective s…

math.OC2014★ 84 cited

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…