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Ordering Structures and Their Applications

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Applications of Nonlinear Analysis

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 134))

Abstract

Ordering structures play a fundamental role in many mathematical areas. These include important topics in optimization theory such as vector optimization and set optimization, but also other subjects as decision theory use ordering structures as well. Due to strong connections between ordering structures and cones in the considered space, order theory is also used every time two elements of a space, which is more general than the real line, are compared with each other. Therefore, also cone programming possessing restrictions defined using cones, and especially semidefinite optimization where the variables are symmetric matrices, make use of ordering structures. These structures may, on the one hand, be independent of the considered element of a given space or, on the other hand, vary for each element of this space. In the last case, we speak of variable ordering structures, which is one of the important topics in the newest research on vector optimization.

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Eichfelder, G., Pilecka, M. (2018). Ordering Structures and Their Applications. In: Rassias, T. (eds) Applications of Nonlinear Analysis . Springer Optimization and Its Applications, vol 134. Springer, Cham. https://doi.org/10.1007/978-3-319-89815-5_9

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