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Thread Subject:
Matrix function Optimization

Subject: Matrix function Optimization

From: Dahnial

Date: 24 Dec, 2013 07:18:06

Message: 1 of 7

Hello!
I have a problem about optimization for a matrix.
let say
C.A = F, where C is symmetric 2x2 matrix consisting variable c1 and c2, [c1 0; 0 c2]
and F is just matrix consisting of constant numbers

then i can say
A=C^-1.F (yes, it is just an inverse matrix of C)

here comes my problem:
i want to find optimum value for C1 and C2 to minimize A (by optimization)
the contraint for each C1 and C2 is, let say 0<C1<10
and i have the initial value for c1 and c2

i have looked some of references and some of them stated that it should be done by lagrangian optimization in quadratic programming

i know a bit about linear optimization. but this problem is beyond my knowledge, especially when matrix comes in the equation

How can I do that?
Thanks a lot, and sorry: I am a newbie in optimization.
best regards,
Dahnial S

Subject: Matrix function Optimization

From: Bruno Luong

Date: 24 Dec, 2013 08:24:05

Message: 2 of 7

"Dahnial" wrote in message <l9bcfe$78a$1@newscl01ah.mathworks.com>...
> Hello!
> I have a problem about optimization for a matrix.
> let say
> C.A = F, where C is symmetric 2x2 matrix consisting variable c1 and c2, [c1 0; 0 c2]
> and F is just matrix consisting of constant numbers
>
> then i can say
> A=C^-1.F (yes, it is just an inverse matrix of C)
>
> here comes my problem:
> i want to find optimum value for C1 and C2 to minimize A (by optimization)
> the contraint for each C1 and C2 is, let say 0<C1<10
> and i have the initial value for c1 and c2
>

Optimization problem where variable is defined on an open interval (<) is usually incorrect stated, since there will be no solution.

Bruno

Subject: Matrix function Optimization

From: John D'Errico

Date: 24 Dec, 2013 15:21:05

Message: 3 of 7

"Dahnial" wrote in message <l9bcfe$78a$1@newscl01ah.mathworks.com>...
> Hello!
> I have a problem about optimization for a matrix.
> let say
> C.A = F, where C is symmetric 2x2 matrix consisting variable c1 and c2, [c1 0; 0 c2]
> and F is just matrix consisting of constant numbers
>
> then i can say
> A=C^-1.F (yes, it is just an inverse matrix of C)
>
> here comes my problem:
> i want to find optimum value for C1 and C2 to minimize A (by optimization)
> the contraint for each C1 and C2 is, let say 0<C1<10
> and i have the initial value for c1 and c2
>
> i have looked some of references and some of them stated that it should be done by lagrangian optimization in quadratic programming
>
> i know a bit about linear optimization. but this problem is beyond my knowledge, especially when matrix comes in the equation
>
> How can I do that?
> Thanks a lot, and sorry: I am a newbie in optimization.
> best regards,
> Dahnial S

How do you intend to minimize a matrix A?

You must define your intent, else nothing can be done.

John

Subject: Matrix function Optimization

From: Dahnial

Date: 25 Dec, 2013 00:36:13

Message: 4 of 7

"Bruno Luong" <b.luong@fogale.findmycountry> wrote in message
> Optimization problem where variable is defined on an open interval (<) is usually incorrect stated, since there will be no solution.
>
> Bruno

Hi Bruno,
thanks for your response

but the constraint is in a closed interval, between 0 and 10 and not the open one (all the real value).
i should say, i simplify my question. my actual constraint for C1 is: 0.1 of the initial value until 10 times the initial value
but i think it is too complex, so i just ask 0<C1<10

thanks
Dahnial

Subject: Matrix function Optimization

From: Dahnial

Date: 25 Dec, 2013 00:40:14

Message: 5 of 7

"John D'Errico" <woodchips@rochester.rr.com> wrote in message <l9c8p1$sl0$1@newscl01ah.mathworks.com>...
> "Dahnial" wrote in message <l9bcfe$78a$1@newscl01ah.mathworks.com>...
>
> How do you intend to minimize a matrix A?
>
> You must define your intent, else nothing can be done.
>
> John

Hi John,
thanks for your response.

i am sorry, what do you mean by "how do you intend"?
my actual problem is more complex than the one that i ask, so maybe i skipped some information
for matrix A, i just have to make it tends to zero
and find C1, C2 (within the constraint) that make the matrix A tends to zero

thanks
Dahnial

Subject: Matrix function Optimization

From: Bruno Luong

Date: 25 Dec, 2013 11:22:06

Message: 6 of 7

"Dahnial" wrote in message <l9d99t$oid$1@newscl01ah.mathworks.com>...
> "Bruno Luong" <b.luong@fogale.findmycountry> wrote in message
> > Optimization problem where variable is defined on an open interval (<) is usually incorrect stated, since there will be no solution.
> >
> > Bruno
>
> Hi Bruno,
> thanks for your response
>
> but the constraint is in a closed interval, between 0 and 10 and not the open one (all the real value).
> i should say, i simplify my question. my actual constraint for C1 is: 0.1 of the initial value until 10 times the initial value
> but i think it is too complex, so i just ask 0<C1<10

This 0 < C1 < 10 an open interval. 0.1*a <= C1 * 10*a is a close interval, whatever the value of a. Pick your choice. Simplify the problem as you did just make a well-posed problem to an ill-posed one.

Bruno

Subject: Matrix function Optimization

From: Dahnial

Date: 25 Dec, 2013 13:29:08

Message: 7 of 7

"Bruno Luong" <b.luong@fogale.findmycountry> wrote in message <l9ef4u$ad2$1@newscl01ah.mathworks.com>...
> "Dahnial" wrote in message <l9d99t$oid$1@newscl01ah.mathworks.com>...
> This 0 < C1 < 10 an open interval. 0.1*a <= C1 * 10*a is a close interval, whatever the value of a. Pick your choice. Simplify the problem as you did just make a well-posed problem to an ill-posed one.
>
> Bruno

Hi Bruno,
Thanks for your response
Then my apologize to mistakenly state my problem.
and yes, the real constraint about my problem is:
(let say the initial value of C1 is a)
0.1*a < C1 < 10*a
so that means C1 can be any value inside that interval. can we say this as a closed interval?

do you have any suggestion on how should i do my problem(optimize the function-that contains matrix)?

thank you
Dahnial

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