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
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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:
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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
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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:
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