On some properties of finite sums of ridge functions defined on convex subsets of ℝ n
Necessary conditions are established for the continuity of finite sums of ridge functions defined on convex subsets E of the space R n . It is shown that under some constraints imposed on the summed functions ϕ i , in the case when E is open, the continuity of the sum implies the continuity of all ϕ i . In the case when E is a convex body with nonsmooth boundary, a logarithmic estimate is obtained for the growth of the functions ϕ i in the neighborhoods of the boundary points of their domains of definition. In addition, an example is constructed that demonstrates the accuracy of the estimate obtained.
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- 16.F. P. Vasil’ev, Optimization Methods (Faktorial, Moscow, 2002) [in Russian].Google Scholar