- #1
dilbert2011
- 3
- 0
Hi all,
I am working on a project and stuck at the following problem.
Find vector [tex]x_{n\times 1}[/tex] which minimizes the function
subject to the linear equality constraint
The function f(x) trivially has a minimum value of 0 for x = 0. The equality constraint is an under determined problem with multiple solutions. One of the possible solutions is certain to minimize f(x). So I am relatively certain that solution to this problem exists. The additional issue is that the rank of matrix A could be less than m. So the standard Lagrange multipliers approach does not work in this case.
Any suggestions on how to approach this problem ?
I am working on a project and stuck at the following problem.
Find vector [tex]x_{n\times 1}[/tex] which minimizes the function
Code:
[tex]f(x) = \sum_{i}^{n}x_{i}^{2}[/tex]
subject to the linear equality constraint
Code:
[tex][A]_{m\times n} x_{n \times 1}=b_{m\times 1}[/tex] with [tex]m\leq n[/tex]
The function f(x) trivially has a minimum value of 0 for x = 0. The equality constraint is an under determined problem with multiple solutions. One of the possible solutions is certain to minimize f(x). So I am relatively certain that solution to this problem exists. The additional issue is that the rank of matrix A could be less than m. So the standard Lagrange multipliers approach does not work in this case.
Any suggestions on how to approach this problem ?