Strong and Weak Convexity in Nonlinear Differential Games

Ivanov, Grigorii Evgen'evich; Golubev, Maxim O.

doi:10.1016/j.ifacol.2018.11.345

Cited by 6 publications

(1 citation statement)

References 4 publications

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“…Теорему 2.1 можно применять и для других классов так называемых обобщенно выпуклых множеств (см., напр., [5,9,[13][14][15]). Заметим, что теорему 2.1 можно обобщить на случай трехмерного пространства, если подходящим образом определить трехмерный аналог крышки кармана.…”

Section: заключениеunclassified

On the guaranteed estimates of the area of convex subsets of compacts on a plane

Ушаков¹,

Ершов²,

Ershov³

2020

MGTA

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The paper considers the problem of constructing a convex subset of the largest area in a nonconvex compact on the plane, as well as the problem of constructing a convex subset from which the Hausdorff deviation of the compact is minimal. Since, in the general case, the exact solution of these problems is impossible, the geometric difference between the convex hull of a compact and a circle of a certain radius is proposed as an acceptable replacement for the exact solution. A lower bound for the area of this geometric difference and an upper bound for the Hausdorff deviation from it of a given nonconvex compact set are obtained. As examples, we considered the problem of constructing convex subsets from an alpha-set and a set with a finite Mordell concavity coefficient.

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Section: заключениеunclassified