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Set approach for set optimization with variable ordering structures. I: Set relations and relationship to vector approach. (English) Zbl 1354.49035

Summary: This paper aims at combining variable ordering structures with set relations in set optimization, which have been defined using the constant ordering cone before. We provide several new set relations in the context of variable ordering structures, discuss their usefulness, and give different examples from a practical point of view. After analyzing the properties of the introduced relations, we define solution notions for set-valued optimization problems equipped with variable ordering structures. We also relate these new notions to those ones obtained by the so-called vector approach.

MSC:

49J53 Set-valued and variational analysis
90C29 Multi-objective and goal programming
90C30 Nonlinear programming
54C60 Set-valued maps in general topology

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References:

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