## Invited Session Wed.3.H 1029

#### Wednesday, 15:15 - 16:45 h, Room: H 1029

**Cluster 15: Multi-objective optimization** [...]

### Applications of vector and set optimization

**Chair: Andreas Löhne**

**Wednesday, 15:15 - 15:40 h, Room: H 1029, Talk 1**

**Sonia Radjef**

The direct support method to solve a linear multiobjective problem with bounded variables

**Coauthor: Mohand Ouamer Bibi**

**Abstract:**

We propose a new efficient method for defining the solution set of a multiobjective problem, where the objective functions involved are linear, the set of feasible points is a set of linear constraints and the decision variables are

are upper and lower bounded. The algorithm is a generalization of the direct support method, for solution a linear mono-objective program. Its particularity is that it avoids the

preliminary transformation of the decision variables. It handles the bounds such as they are initially formulated. The method is really effective, simple to use and permits to speed-up the resolution process. We use the suboptimal criterion of the method in single-objective programming to find the subefficient extreme points and the subweakly efficient extreme

points of the problem. This algorithm is applied to solve a problem of production planning in the Ifri Dairy.

**Wednesday, 15:45 - 16:10 h, Room: H 1029, Talk 2**

**Andreas Löhne**

BENSOLVE - A solver for multi-objective linear programs

**Abstract:**

BENSOLVE is a MOLP solver based on Benson's outer approximation algorithm and its dual variant. The algorithms are explained and the usage of the solver is demonstrated by different applications, among them applications from Mathematical Finance concerning markets with transaction costs.

**Wednesday, 16:15 - 16:40 h, Room: H 1029, Talk 3**

**Firdevs Ulus**

An approximation algorithm for convex vector optimization problems and its application in finance

**Coauthors: Andreas Löhne, Birgit Rudloff**

**Abstract:**

Linear vector optimization problems (VOP) are well studied

in the literature, and recently there are studies on approximation

algorithms for convex VOP. We propose an approximation algorithm for

convex VOP, which is an extension of Benson’s outer approximation and

provides both inner and outer approximation for the convex optimal

frontier. The algorithm requires solving only one optimization problem

in each iteration step, rather than two as in the literature. We also

extend the algorithm to arbitrary solid polyhedral ordering cones. As

a financial application, we consider a discrete time market model for

d-asset, with proportional transaction costs, over a finite

probability space. In this setting, we study the set valued approach

for utility maximization, and show that this problem can be solved by

reformulating it as a convex VOP and applying the proposed algorithm.