由买买提看人间百态

boards

本页内容为未名空间相应帖子的节选和存档,一周内的贴子最多显示50字,超过一周显示500字 访问原贴
Mathematics版 - a question about optimization
相关主题
help on an optimization problemfinding the maximal angle between a vector and a subspace
谁见过类似的dynamic programming (or combinatorial optimization)问题?请教一个概率问题
optimization问题请指教关于ODE名词的一个问题
请问有那种optimization是解决变化的objective function的?如何判断 A - B 是一个PSD矩阵?
MDP如果不知道reward function怎么办?紧急求助,求一个函数的表达式,对数学系的人来说应该是小case
An expectation problemRelation between information and entropy
[合集] An expectation problem求文章 Correction to “entropy and maximal spacings for random partitions”
choose k points with maximum pairwise distances惜才有品位的个大富翁也不少
相关话题的讨论汇总
话题: xi话题: two话题: problem话题: objective话题: objectives
进入Mathematics版参与讨论
1 (共1页)
l***o
发帖数: 6
1
Hi there,
Sorry I can't input Chinese right now.
Please help me with the following question. Thank you so much!
To solve a problem, I have two objectives:
1. choose xi to max f(xi),
2. choose xi to min g(xi).
where f(x) and g(x) are two functions of x.
Since there are two objectives, I want to combine them to one objective
function to ease the problem.
Two possible choices of the objective functions are:
1. choose xi to max[f(xi) - g(xi)],
2. choose xi to max[ f(xi)/g(xi) ].
My question is: will
N***l
发帖数: 52
2
i think the problem is the optimizer for f and g may be different,
and if they ARE different, any composite objective function can only
be a ``guess" of the solution, actually there is no such thing as
``the" solution in your problem.
As in the f-g case, you are maximizing the difference, but the thing
is the maximizer for the difference function may not simultaneously
maximize f and minimize g, all you know is it maximize the difference.
I think there is no best solution in general, but in your

【在 l***o 的大作中提到】
: Hi there,
: Sorry I can't input Chinese right now.
: Please help me with the following question. Thank you so much!
: To solve a problem, I have two objectives:
: 1. choose xi to max f(xi),
: 2. choose xi to min g(xi).
: where f(x) and g(x) are two functions of x.
: Since there are two objectives, I want to combine them to one objective
: function to ease the problem.
: Two possible choices of the objective functions are:

l***o
发帖数: 6
3
Yeah, you are right! There is a compromise bwtween maxf(x) and maxg(x) for my
problem.
So the 1st objective function maximize the absolute difference, and the 2nd
objective function maximize the proportional difference, right?

【在 N***l 的大作中提到】
: i think the problem is the optimizer for f and g may be different,
: and if they ARE different, any composite objective function can only
: be a ``guess" of the solution, actually there is no such thing as
: ``the" solution in your problem.
: As in the f-g case, you are maximizing the difference, but the thing
: is the maximizer for the difference function may not simultaneously
: maximize f and minimize g, all you know is it maximize the difference.
: I think there is no best solution in general, but in your

N***l
发帖数: 52
4
according to your definition, yes.

my

【在 l***o 的大作中提到】
: Yeah, you are right! There is a compromise bwtween maxf(x) and maxg(x) for my
: problem.
: So the 1st objective function maximize the absolute difference, and the 2nd
: objective function maximize the proportional difference, right?

l***o
发帖数: 6
5
Thank you!
You only mentioned the linear combination of the two functions, but not the
nonlinear combination, such as f(x)/g(x). Is this combination correct?
N***l
发帖数: 52
6
I think there are counter examples (bad examples) for both of your
composite ``optimal" objectives.

Hi there,
Sorry I can't input Chinese right now.
Please help me with the following question. Thank you so much!
To solve a problem, I have two objectives:
1. choose xi to max f(xi),
2. choose xi to min g(xi).
where f(x) and g(x) are two functions of x.
Since there are two objectives, I want to combine them to one objective
function to ease the problem.
Two possible choices of the objective functi

【在 l***o 的大作中提到】
: Hi there,
: Sorry I can't input Chinese right now.
: Please help me with the following question. Thank you so much!
: To solve a problem, I have two objectives:
: 1. choose xi to max f(xi),
: 2. choose xi to min g(xi).
: where f(x) and g(x) are two functions of x.
: Since there are two objectives, I want to combine them to one objective
: function to ease the problem.
: Two possible choices of the objective functions are:

D*******a
发帖数: 3688
7
you can do whatever you want as long as it is meaningful
for linear, you can view 'a' as a price

【在 l***o 的大作中提到】
: Thank you!
: You only mentioned the linear combination of the two functions, but not the
: nonlinear combination, such as f(x)/g(x). Is this combination correct?

s***t
发帖数: 113
8
You also need to think about how to solve the resulted model.
In general, f(x) - g(x) is much easier than f(x)/g(x). You can also
model the problem in 2-level optimization problem, e.g.,
min g(x)
s.t. max f(x)
s.t. x \in X
The resultant problem is however usually very hard to solve.

【在 l***o 的大作中提到】
: Hi there,
: Sorry I can't input Chinese right now.
: Please help me with the following question. Thank you so much!
: To solve a problem, I have two objectives:
: 1. choose xi to max f(xi),
: 2. choose xi to min g(xi).
: where f(x) and g(x) are two functions of x.
: Since there are two objectives, I want to combine them to one objective
: function to ease the problem.
: Two possible choices of the objective functions are:

l***o
发帖数: 6
9
Yeah, you are right! There is a compromise bwtween maxf(x) and maxg(x) for my
problem.
So the 1st objective function maximize the absolute difference, and the 2nd
objective function maximize the proportional difference, right?

【在 N***l 的大作中提到】
: i think the problem is the optimizer for f and g may be different,
: and if they ARE different, any composite objective function can only
: be a ``guess" of the solution, actually there is no such thing as
: ``the" solution in your problem.
: As in the f-g case, you are maximizing the difference, but the thing
: is the maximizer for the difference function may not simultaneously
: maximize f and minimize g, all you know is it maximize the difference.
: I think there is no best solution in general, but in your

l***o
发帖数: 6
10
So you mean that the two objective functions are not equal and may give
different results for a given problem?

【在 N***l 的大作中提到】
: I think there are counter examples (bad examples) for both of your
: composite ``optimal" objectives.
:
: Hi there,
: Sorry I can't input Chinese right now.
: Please help me with the following question. Thank you so much!
: To solve a problem, I have two objectives:
: 1. choose xi to max f(xi),
: 2. choose xi to min g(xi).
: where f(x) and g(x) are two functions of x.

D*******a
发帖数: 3688
11
you can do whatever you want as long as it is meaningful
for linear, you can view 'a' as a price

【在 l***o 的大作中提到】
: Thank you!
: You only mentioned the linear combination of the two functions, but not the
: nonlinear combination, such as f(x)/g(x). Is this combination correct?

w******o
发帖数: 442
12
f(xi)/g(xi) is good for persentage change.
f(xi)-g(xi) is good for aboslute value change.
It depend on which one do you preffer (persentage or aboslute value), which is
better.

【在 l***o 的大作中提到】
: Hi there,
: Sorry I can't input Chinese right now.
: Please help me with the following question. Thank you so much!
: To solve a problem, I have two objectives:
: 1. choose xi to max f(xi),
: 2. choose xi to min g(xi).
: where f(x) and g(x) are two functions of x.
: Since there are two objectives, I want to combine them to one objective
: function to ease the problem.
: Two possible choices of the objective functions are:

D*******a
发帖数: 3688
13
there is a trade off between two objectives
usually, you can combine them like
max f(x)-a*g(x)
or
max f(x)
s.t. g(x)>b
there is no universal rules

【在 l***o 的大作中提到】
: Hi there,
: Sorry I can't input Chinese right now.
: Please help me with the following question. Thank you so much!
: To solve a problem, I have two objectives:
: 1. choose xi to max f(xi),
: 2. choose xi to min g(xi).
: where f(x) and g(x) are two functions of x.
: Since there are two objectives, I want to combine them to one objective
: function to ease the problem.
: Two possible choices of the objective functions are:

w****r
发帖数: 1046
14
You may take derivative with respect to xi to find your optimum f and g. But
the values of xi for the two optimization functions may differ.
Well, the optimum solution for maximizing the function of f(x)-g(x) probably
does not optimize f and g, simutaneously. Sometimes, it does.
Your problem is very similar to firm theory in microeconomics.
1 (共1页)
进入Mathematics版参与讨论
相关主题
惜才有品位的个大富翁也不少MDP如果不知道reward function怎么办?
A problem on a dynamic process of positive semi-definite mAn expectation problem
请教一个概率问题[合集] An expectation problem
How to define a coproduct ofchoose k points with maximum pairwise distances
help on an optimization problemfinding the maximal angle between a vector and a subspace
谁见过类似的dynamic programming (or combinatorial optimization)问题?请教一个概率问题
optimization问题请指教关于ODE名词的一个问题
请问有那种optimization是解决变化的objective function的?如何判断 A - B 是一个PSD矩阵?
相关话题的讨论汇总
话题: xi话题: two话题: problem话题: objective话题: objectives