CG versus BFGS for iterative linear solvers - 未名空间MITBBS历史存档

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CG versus BFGS for iterative linear solvers

CG versus BFGS for iterative linear solvers# Computation - 科学计算

y*i2008-02-15 08:02

1 楼

感觉写得比较浅显，比较宏观的样子。。。

h*z2008-02-15 08:02

2 楼

It seems like most of the iterative linear solvers out there are either
based on or closely related to the conjugate gradient method. I know it's
commonly believed that BFGS is superior to CG as an unconstrained
optimization algorithm, so I'm wondering why all the iterative solvers are
based on CG type of algorithms?

l*i2008-02-15 08:02

3 楼

You can do preconditioning in CG, while it's not so straightforward in the c
ase of BFGS or LBFGS. Who said BGFS is superior to CG as an unconstrained op
timization algorithm?

are

【在 h***z 的大作中提到】

: It seems like most of the iterative linear solvers out there are either
: based on or closely related to the conjugate gradient method. I know it's
: commonly believed that BFGS is superior to CG as an unconstrained
: optimization algorithm, so I'm wondering why all the iterative solvers are
: based on CG type of algorithms?

h*z2008-02-15 08:02

4 楼

Thanks for your reply. So what makes preconditioning difficult for BFGS?
In any case, my problem doesn't need preconditioning and only an approximate
solution is needed. What would be the advantage of using CG type of
methods (if any) in this case?
I don't know if there's any definitive studies, but it's a widely-held folk-
wisdom in the fields (EE/CS) that I've worked in that BFGS is faster and
more robust than CG. My own limited experience with CG and BFGS agrees with
this as well, though

【在 l*****i 的大作中提到】

: You can do preconditioning in CG, while it's not so straightforward in the c
: ase of BFGS or LBFGS. Who said BGFS is superior to CG as an unconstrained op
: timization algorithm?
:
: are