A quick guide about solving equations (optimization problem)

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Matin Kh
Matin Kh 2014-1-7
评论： Matin Kh 2014-6-15
Assume x is a vector of size n. It is a sample.
beta are some vectors of size n. Each beta_j is a vector. There are s different *beta*s.
a_j is a real number. a contains all s numbers related to a sample ( x ).
alpha is a known parameter. Lets assume it is one.
beta is known, so is x. By solving the following equation, we find a_hat which contains the proper coefficients. enter image description here I need to know whether this equation can be solved in MATLAB.
  1 个评论
Image Analyst
Image Analyst 2014-1-8
How is this "a quick guide"? It doesn't seem to guide or help anybody. It doesn't look like a guide at all, but instead looks like your homework. Is it your homework? If so you should tag it as homework.

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采纳的回答

John D'Errico
John D'Errico 2014-1-8
A classic (and simple, even trivial) ridge regression problem, IF it were a 2 norm on a.
No toolbox would even be needed. Convert it into a simple regression problem, by augmenting your design matrix with sqrt(alpha)*eye(s). Solve using backslash. WTP?
As a 1 norm on a, so with mixed norms, you probably need to solve this using the optimization toolbox, so fminunc. Still easy enough. Read through the examples for fminunc. Still WTP?
Not sure why you feel the need to mix your norms anyway.

更多回答（2 个）

Matt J
Matt J 2014-1-8
编辑：Matt J 2014-1-8
You can reformulate as a smooth problem in unknowns a(i), r(i)
min norm(x-beta*a)^2 + alpha*sum(r)
with constraints
-r(i)<=a(i)<=r(i)
This could be solved with quadprog or fmincon
Marc
Marc 2014-1-8
Yes this problem can be solved with functions in the optimization toolbox.

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