On polynomial solvability of some vector subset problems in Euclidean space with fixed dimension

Problems of choosing vectors in the multidimensional Euclidean space $\mathbb R^k$ are considered. The maximum norm of sum or the averaged square of the norm are considered as the problem objective. We present combinatorial algorithms with time complexity $O(k^2n^{2k})$. Thereby it is shown that the considered problems are polynomially solvable for fixed dimension of space $\mathbb R^k$. Bibl. 6.