Linear least-square optimization problem, help!

Hi, I'm stuck in one optimization problem by using Matlab. The problem is defined as below.

X1 (361 by 361) * lambda (361 by 1) = Y1 (361 by 1)

X2 (361 by 361) * lambda (361 by 1) = Y2 (361 by 1)

X3 (361 by 361) * lambda (361 by 1) = Y3 (361 by 1)

...

X158 (361 by 361) * lambda (361 by 1) = Y158 (361 by 1)

I'm trying to find the optimal non-negative lambda minimizing the sum of squared error between Y and predicted Y. And, I have 158 examples. Please give any clues to solve this problem!

Answer 1

[John D'Errico]

WTP? If it is the same vector lambda that must apply to all cases, then you have ONE nonnegative (but linear) least squares problem, with 361*150 rows, and 361 columns.

Concatenate the matrices into ONE array. Then call lsqnonneg.

This is NOT an optimization problem. Only lsqnonneg is required.

And, by the way, next time, don't be foolish and create numbered variables. Instead, learn to use multidimensional arrays or cell arrays. Your code will improve, making this into a trivial problem.

[HOJIN JANG]

You're right, it can be solved by just concatenating all of samples and using lsqnonneg. Thanks!