Tips for optimisation problem
$begingroup$
I have an optimization (minimize) problem which can be written down as:
$f(vec{x})=sum_1^m{(max(vec{a_1}*x_1,vec{a_2}*x_2,vec{a_3}*x_3,...,vec{a_n}*x_n)-vec{a_0})^2}$
Where $m$ is the size of those vectors $vec{a_i}$ and $n$ is the number of them. The max operation is across the ROWS of the matrix formed by tiling all the a_n column vectors. The sum is across all the components of the final vector containing the squared errors, I didn't know how to indicate that... Basically the result of the max operation is a vector which must be as close to a_0 as possible.
I need some tips in minimizing this, numerical solutions are completely fine, everything is already in a matlab code. $m$ is around 100 and $n$ around 1000.
I'm currently experimenting with Genetic Algorithms but I feel that there is a more clever way, given the simpleness of the function!
Thanks a lot,
Michele
optimization numerical-linear-algebra least-squares
asked Dec 22 '18 at 11:41
MicheleMichele
12
$endgroup$
add a comment |
$begingroup$
I have an optimization (minimize) problem which can be written down as:
$f(vec{x})=sum_1^m{(max(vec{a_1}*x_1,vec{a_2}*x_2,vec{a_3}*x_3,...,vec{a_n}*x_n)-vec{a_0})^2}$
Where $m$ is the size of those vectors $vec{a_i}$ and $n$ is the number of them. The max operation is across the ROWS of the matrix formed by tiling all the a_n column vectors. The sum is across all the components of the final vector containing the squared errors, I didn't know how to indicate that... Basically the result of the max operation is a vector which must be as close to a_0 as possible.
I need some tips in minimizing this, numerical solutions are completely fine, everything is already in a matlab code. $m$ is around 100 and $n$ around 1000.
I'm currently experimenting with Genetic Algorithms but I feel that there is a more clever way, given the simpleness of the function!
Thanks a lot,
Michele
optimization numerical-linear-algebra least-squares
asked Dec 22 '18 at 11:41
MicheleMichele
12
$endgroup$
add a comment |
$begingroup$
I have an optimization (minimize) problem which can be written down as:
$f(vec{x})=sum_1^m{(max(vec{a_1}*x_1,vec{a_2}*x_2,vec{a_3}*x_3,...,vec{a_n}*x_n)-vec{a_0})^2}$
Where $m$ is the size of those vectors $vec{a_i}$ and $n$ is the number of them. The max operation is across the ROWS of the matrix formed by tiling all the a_n column vectors. The sum is across all the components of the final vector containing the squared errors, I didn't know how to indicate that... Basically the result of the max operation is a vector which must be as close to a_0 as possible.
I need some tips in minimizing this, numerical solutions are completely fine, everything is already in a matlab code. $m$ is around 100 and $n$ around 1000.
I'm currently experimenting with Genetic Algorithms but I feel that there is a more clever way, given the simpleness of the function!
Thanks a lot,
Michele
optimization numerical-linear-algebra least-squares
asked Dec 22 '18 at 11:41
MicheleMichele
12
$endgroup$
I have an optimization (minimize) problem which can be written down as:
$f(vec{x})=sum_1^m{(max(vec{a_1}*x_1,vec{a_2}*x_2,vec{a_3}*x_3,...,vec{a_n}*x_n)-vec{a_0})^2}$
Where $m$ is the size of those vectors $vec{a_i}$ and $n$ is the number of them. The max operation is across the ROWS of the matrix formed by tiling all the a_n column vectors. The sum is across all the components of the final vector containing the squared errors, I didn't know how to indicate that... Basically the result of the max operation is a vector which must be as close to a_0 as possible.
I need some tips in minimizing this, numerical solutions are completely fine, everything is already in a matlab code. $m$ is around 100 and $n$ around 1000.
I'm currently experimenting with Genetic Algorithms but I feel that there is a more clever way, given the simpleness of the function!
Thanks a lot,
Michele
optimization numerical-linear-algebra least-squares
optimization numerical-linear-algebra least-squares
asked Dec 22 '18 at 11:41
MicheleMichele
12
asked Dec 22 '18 at 11:41
MicheleMichele
12
edited Jan 7 at 12:53
Michele
asked Dec 22 '18 at 11:41
MicheleMichele
12
asked Dec 22 '18 at 11:41
MicheleMichele
12
asked Dec 22 '18 at 11:41
MicheleMichele
12
12
add a comment |
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