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Published: July 19,2024

Since the convex set plays an important role in many mathematical branches such as convex optimization and computer aided geometry design, it is of great significance to investigate the properties of convex sets, especially the geometric structures of convex sets. In a relatively general setting, this paper investigates the geometric boundary of some convex sets defined in terms of two given symmetric positive semi-definite matrices *A* and *B* when these two matrices have some special forms. Especially, when *A* and *B* are both diagonal or when they commute each other, several interesting theorems are established and the corresponding geometric boundaries are characterized. For a more general setting when *A* is symmetric positive semi-definite and *B* is diagonal, although general theorems are not obtained, an interesting example is studied in detail. The graph of the corresponding boundary is plotted to inspire interested readers to gain a deeper insight into this problem.

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**On the Geometric Boundary of Some Convex Sets**

**How to cite this paper:** Bo Yu, Zabihullah Omari. (2024) On the Geometric Boundary of Some Convex Sets. *Journal of Applied Mathematics and Computation*, **8**(**2**), 166-176.

DOI: http://dx.doi.org/10.26855/jamc.2024.06.010

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