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EE版 - any optimization theory guru here?
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进入EE版参与讨论
1 (共1页)
j*******e
发帖数: 586
1
can any optimization guru here give me some hints please? I don't know if my
question is just a trivial one in expert's eyes. But here it is:
my objective function f(x) is a scalar function of a vector x of length n. I
know that if x* is a solution, then cx* must also be a solution, where c is
a real constant. This actually reduces the n-dimensional problem to a n-1
dimension one. Is there any difference between the following two strategies:
(1) treat the problem as an unconstrained optimization
D*******a
发帖数: 3688
2
(2) is not difficult because you can easily project back onto the unit
sphere if you violate the constraint.

my
I
is
strategies:

【在 j*******e 的大作中提到】
: can any optimization guru here give me some hints please? I don't know if my
: question is just a trivial one in expert's eyes. But here it is:
: my objective function f(x) is a scalar function of a vector x of length n. I
: know that if x* is a solution, then cx* must also be a solution, where c is
: a real constant. This actually reduces the n-dimensional problem to a n-1
: dimension one. Is there any difference between the following two strategies:
: (1) treat the problem as an unconstrained optimization

j*******e
发帖数: 586
3
do you mean (2) is better in terms of the ability of finding the solution?

【在 D*******a 的大作中提到】
: (2) is not difficult because you can easily project back onto the unit
: sphere if you violate the constraint.
:
: my
: I
: is
: strategies:

a*******x
发帖数: 47
4
I donot like (2), there the feasible zone becomes a infinitely thin shell
which is hostile to many solvers.
I would reformulate the prob. as:
F=f(x(1:n-1), sqrt(1-sum(x(1:n-1).^2)))
where sum(x(1:n-1).^2) <=1

my
I
is
strategies:

【在 j*******e 的大作中提到】
: can any optimization guru here give me some hints please? I don't know if my
: question is just a trivial one in expert's eyes. But here it is:
: my objective function f(x) is a scalar function of a vector x of length n. I
: know that if x* is a solution, then cx* must also be a solution, where c is
: a real constant. This actually reduces the n-dimensional problem to a n-1
: dimension one. Is there any difference between the following two strategies:
: (1) treat the problem as an unconstrained optimization

D*******a
发帖数: 3688
5
equality constraints are much easier to manipulate than inequality
constraints.

【在 a*******x 的大作中提到】
: I donot like (2), there the feasible zone becomes a infinitely thin shell
: which is hostile to many solvers.
: I would reformulate the prob. as:
: F=f(x(1:n-1), sqrt(1-sum(x(1:n-1).^2)))
: where sum(x(1:n-1).^2) <=1
:
: my
: I
: is
: strategies:

1 (共1页)
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话题: guru话题: here话题: any话题: solution