→ kane950544 :convex cone的定義是?? 10/22 19:20
1. Show that C is a convex cone if and only if x and y 屬於 C
imply that λx + μy 屬於 C for λ≧ 0 and μ≧ 0
2. {x: Ax ≦ b , x ≧ 0 } ,where A is m ×n matrix and b is
an m vector .
please proof x is convex set ?
3. Which of the following sets are convex and which are not?
(a) {(X1,X2,X3):X2 ≧ X1^2 , x1+2 X2+ X3 ≦ 4}
(b) {(X1,X2): X1=3 ,|X2|≦4}
(c) {(X1,X2,X3):X3 = |X2|, X1≦3}
因為凸函數與凸組合的概念不夠清楚, 很需要眾高手的協助!
十分感謝大家的幫忙!
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