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any optimization theory guru here?

any optimization theory guru here?# EE - 电子工程

j*e2007-10-09 07:10

1 楼

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*a2007-10-09 07:10

2 楼

(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*e2007-10-09 07:10

3 楼

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*x2007-10-09 07:10

4 楼

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】

D*a2007-10-09 07:10

5 楼

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: