Crumple
发表于 2025-3-25 03:57:00
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王得到
发表于 2025-3-25 11:02:56
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增强
发表于 2025-3-25 12:02:26
Sufficient Extremum Conditions. Examples,We now apply the results of the preceding lecture to various problems.
Biguanides
发表于 2025-3-25 17:26:59
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藐视
发表于 2025-3-25 20:52:11
Introduction,systematized and brought together under the heading of the ., with its innumerable applications to physics and mechanics. Attention was devoted principally to the analysis of . and . defined over the entire space or restricted to some smooth manifold. The extremum conditions in this case are the . (
动物
发表于 2025-3-26 03:42:57
Supporting Hyperplanes and Extremal Points,e closed hyperplane . is called a . for A at the point x.. The geometric sense of a supporting hyperplane is quite simple: the set A lies on one side of the hyperplane and cuts it in one point x. (Fig. 5).
gorgeous
发表于 2025-3-26 05:40:43
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LATE
发表于 2025-3-26 09:56:00
Calculation of Dual Cones,plication of the Dubovitskii-Milyutin theorem to determine necessary conditions for an extremum, it remains to show how one constructs dual cones, This we now proceed to do. Some results in this connection were presented in Lecture 5 (Lemmas 5.2 to 5.10).
Conscientious
发表于 2025-3-26 15:09:33
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adjacent
发表于 2025-3-26 18:35:42
Sufficient Extremum Conditions,re also sufficient. Of course, elementary examples show that in general this is not true. Nevertheless, we shall prove that, under certain additional assumptions, the necessary extremum conditions are also sufficient, in an important class of extremal problems — convex problems. Sufficient condition