Application of Minkowski operators to convex sets

The dissertation investigates the application of Minkowski operators in the theory of convex sets. In particular, the geometric and topological properties of the Minkowski sum and Minkowski difference are studied, and their applications to convex polygons and polyhedra are presented. The theoretical foundations of Minkowski operators are generalized, and explicit computational formulas and algorithms are developed for certain convex sets in $\mathbb{R}^2$, $\mathbb{R}^3$ and $\mathbb{R}^n$. In addition, the problem of determining the Minkowski difference of arbitrary convex compact sets and compact sets in $\mathbb{R}^n$ is solved.