Invited Session Thu.3.H 1029

Thursday, 15:15 - 16:45 h, Room: H 1029

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

Preference structures in multi-objective optimization

 

Chair: Gabriele Eichfelder

 

 

Thursday, 15:15 - 15:40 h, Room: H 1029, Talk 1

Gabriele Eichfelder
A procedure for solving vector optimization problems with a variable ordering structure

 

Abstract:
Vector optimization problems with a variable ordering structure have recently gained interest due to several applications for instance in image registration and portfolio optimization. Here, the elements in the image space are compared using a cone-valued map, called ordering map, which defines an ordering cone for each element of the image space individually. This leads to a binary relation, which is in general not transitive and also not compatible with the linear structure of the space. We present in this talk a numerical method for determining an approximation of the optimal solution set of such (nonlinear and smooth) vector optimization problems.
In a first step, using classical adaptive approximation methods, a superset of the set of optimal solutions is determined. In a second step, using new nonlinear scalarization results for variable ordering structures, the optimal elements are selected. First numerical results are presented.

 

 

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

Behnam Soleimani
Approximate solutions of vector optimization with variable order structure

 

Abstract:
We introduce concepts for approximate minimal and nondominate solutions of vector optimization problems with variable order structure. Furthermore, we introduce a scalarization method by means of nonlinear functionals and present a characterization of approximate minimal and nondominate solution by using this scalarization method.

 

 

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

Refail Kasimbeyli
Characterization of properly nondominated elements in vector optimization with variable ordering structures

 

Abstract:
This paper studies properly nondominated elements in vector optimization problems with variable ordering structures. We introduce several notions for properly nondominated elements and investigate nonlinear scalarization approach for their characterizations. A new concepts presented in the paper are compared to existing in literature ones. The new type of nonlinear scalarizing functions is introduced and their properties are discussed. These functions are used to characterize the properly nondominated elements.

 

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