para convex set in Vietnamese

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1. SEE ALSO: Connected Set, Convex Function, Concave Polygon, Convex Hull, Convex Optimization Theory, Convex Polygon, Delaunay Triangulation, Simply Connected.

2. 1 Convex Sets, and Convex Functions Inthis section, we introduce oneofthemostimportantideas inthe theoryofoptimization, that of a Convex set

3. Convex polygon, a polygon which encloses a Convex set of points; Convex polytope, a polytope with a Convex set of points; Convex metric space, a generalization of the Convexity notion in abstract metric spaces; Convex function, when the line segment between any two

4. Convexity Convex Function: Function f defined on a convex set is convex if f(αx+(1−α)y) ≤ αf(x) +(1−α)f(y) (0 < α < 1) Equivalent definition: Function f is convex if its epigraph is a convex set.

5. A function f: Rn!Ris Convex if its domain is a Convex set and for

6. De nition 4.18 The primal representation represents a Convex set C using its Convex hull: a Convex com-bination of its points

7. The polar of a bounded set is an absolutely convex and absorbing set.

8. Convex set: contains line segment between any two points in the set x1,x2 ∈ C, 0≤ θ ≤ 1 =⇒ θx1+(1−θ)x2 ∈ C examples (one Convex, two nonConvex sets) Convex sets 2–3

9. We can represent a Convex set in two equivalent ways

10. Convex set, containing the whole line segment that joins points

11. Equivalently, a Convex set or a Convex region is a subset that intersect every line into a single line segment (possibly empty).

12. Convex combination and Convex hull Convex combination of x1,

13. Convex meshes can collide with other Convex colliders and non-Convex meshes

14. convex

15. Convex, concave, strictly Convex, and strongly Convex functions First and second order characterizations of Convex functions Optimality conditions for Convex problems 1 Theory of Convex functions 1.1 De nition Let’s rst recall the de nition of a Convex function

16. All profiles convex to super-convex; exceptional muscle development

17. Then, given any (nonempty) subset S of E, there is a smallest Convex set containing S denoted by C(S)(or conv(S)) and called the Convex hull of S (namely, theintersection of all Convex sets containing S).The affine hull of a subset, S,ofE is the smallest affine set contain-

18. A Concave function is also synonymously called Concave downwards, Concave down, convex upwards, convex cap or upper convex.

19. The concave-convex adjustment of contacts in the anterior dental arch with a newly developed set of concave-convex stripping instruments should enable orthodontic crowding problems to be alleviated biomechanically.

20. Convex Hull

21. Convex Polygon Test

22. Convex SETS 95 It is obvious that the intersection of any family (finite or infinite) of Convex sets is Convex

23. Shoulder: thick and convex

24. convex curve radius capability

25. Convex hull point characterization