q**j
发帖数: 10612 | 1 choose x to
min a'x
subject to: x'Ax=c and x>=0.
这里 a is a constant vector, A is a constant positive definite matrix, c is
a positive constant. x is a non-negative vector。
请各位数学大侠帮忙！多谢了。 |
A*******r
发帖数: 768 | 2 等价于在第一象限的圆弧和一个直线的切点
初中数学高维版 |
q**j
发帖数: 10612 | 3 高手，给指点一个close form solution吧？问题很简单，但是俺也不会算呀。多谢了
。 |
N***m
发帖数: 4460 | 4 待定算字?
is
【在 q**j 的大作中提到】
: choose x to
: min a'x
: subject to: x'Ax=c and x>=0.
: 这里 a is a constant vector, A is a constant positive definite matrix, c is
: a positive constant. x is a non-negative vector。
: 请各位数学大侠帮忙！多谢了。
|
r**g
发帖数: 120 | 5 Given that you restrict x to be a non-negative vector: |
r**g
发帖数: 120 | 6 BTW,
if a is also a non-negative vector, then the minimizer x0 is:
x0 = k A^{-1} a
where the constant k is the solution to the equation
x0' A x0 = c.
is
【在 q**j 的大作中提到】
: choose x to
: min a'x
: subject to: x'Ax=c and x>=0.
: 这里 a is a constant vector, A is a constant positive definite matrix, c is
: a positive constant. x is a non-negative vector。
: 请各位数学大侠帮忙！多谢了。
|
q**j
发帖数: 10612 | 7 多谢多谢。我想想再问问题。sadly，for my purpose a is not non-negative. But I
can certainly try to transform it. |
r**g
发帖数: 120 | 8 Actually, I made a mistake:
Instead of checking $a$ is non-negative or not, you need to check the vector
$A^{-1} a$. My previous answer should be changed to |
A*******r
发帖数: 768 | 9 先做一下变量代换就变成圆了
vector
【在 r**g 的大作中提到】
: Actually, I made a mistake:
: Instead of checking $a$ is non-negative or not, you need to check the vector
: $A^{-1} a$. My previous answer should be changed to
|
