- #1
ahmadnajeeb
- 1
- 0
Hi,
I want to know the solution of the following equation.
[tex] a = argmin_{a}[\sum{||a^Tx_i - y_i||^2}+\alpha ||a||^2] \\[/tex]
where [tex]x_i, y_i[/tex] are column vectors of dimensions m and n respectively where [tex]m>n[/tex]. [tex]\alpha[/tex] is a scalar and
[tex]Y = a^T X[/tex] where [tex]X=[x_1 x_2 ... x_k], Y = [y_1 y_2 ... y_k][/tex]
I know that without this constraint [tex]\alpha ||a||^2[/tex], its a simple least square optimization problem and I can solve it using Matlab's inverse operator. I want to use the same inverse operator but don't know how this constraint changes my original model.
I want to know the solution of the following equation.
[tex] a = argmin_{a}[\sum{||a^Tx_i - y_i||^2}+\alpha ||a||^2] \\[/tex]
where [tex]x_i, y_i[/tex] are column vectors of dimensions m and n respectively where [tex]m>n[/tex]. [tex]\alpha[/tex] is a scalar and
[tex]Y = a^T X[/tex] where [tex]X=[x_1 x_2 ... x_k], Y = [y_1 y_2 ... y_k][/tex]
I know that without this constraint [tex]\alpha ||a||^2[/tex], its a simple least square optimization problem and I can solve it using Matlab's inverse operator. I want to use the same inverse operator but don't know how this constraint changes my original model.