i**M
发帖数: 108 | 1 【 以下文字转载自 Mathematics 讨论区 】
发信人: iFEM (莫扎特的音符), 信区: Mathematics
标 题: optimization question
发信站: BBS 未名空间站 (Wed May 25 16:52:30 2011, 美东)
Suppose c(p) is a monotonically dreasing function as shown in the picture. c
is the cost and p is the risk. As p increases, the risk is increasing but
the cost is decreasing. The question is how to minimize the cost and keep
the risk not too high? Thanks! |
s*****w
发帖数: 2065 | 2 你的函数是C=1/p and C>0？
没有constraint？
c
【在 i**M 的大作中提到】
: 【 以下文字转载自 Mathematics 讨论区 】
: 发信人: iFEM (莫扎特的音符), 信区: Mathematics
: 标 题: optimization question
: 发信站: BBS 未名空间站 (Wed May 25 16:52:30 2011, 美东)
: Suppose c(p) is a monotonically dreasing function as shown in the picture. c
: is the cost and p is the risk. As p increases, the risk is increasing but
: the cost is decreasing. The question is how to minimize the cost and keep
: the risk not too high? Thanks!
|
z****e
发帖数: 438 | 3 what do you mean by saying "keep the risk not too high"? This is the
constraint for your optimization problem and you have to be very specific
about it. |
i**M
发帖数: 108 | 4 The cost function is a strictly decreasing fuction of risk. Ppl told me that
I should use utility function to solve this problem. But I have no idea how
to construct an efficient utility function.
It's not a typical optimization problem, coz, I only need to find a balance
of risk and cost.
Thanks a lot |
s*****w
发帖数: 2065 | 5 the question is not well defined.
that
how
balance
【在 i**M 的大作中提到】
: The cost function is a strictly decreasing fuction of risk. Ppl told me that
: I should use utility function to solve this problem. But I have no idea how
: to construct an efficient utility function.
: It's not a typical optimization problem, coz, I only need to find a balance
: of risk and cost.
: Thanks a lot
|
U*****e
发帖数: 2882 | 6 I guess LZ only asks for any reasonable utility function.
you can make it linear: U=-a*cost-risk, or nonlinear: U=-a*cost-risk^n, with
a>0; or log-linear: U= (cost^p)(risk^q), with p,q<0. It is pretty arbitrary
given what LZ tells us. |
i**M
发帖数: 108 | 7
with
arbitrary
Thanks a lot.
【在 U*****e 的大作中提到】
: I guess LZ only asks for any reasonable utility function.
: you can make it linear: U=-a*cost-risk, or nonlinear: U=-a*cost-risk^n, with
: a>0; or log-linear: U= (cost^p)(risk^q), with p,q<0. It is pretty arbitrary
: given what LZ tells us.
|
U*****e
发帖数: 2882 | 8 that is all right.
【在 i**M 的大作中提到】
:
: with
: arbitrary
: Thanks a lot.
|
