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Cross Validated

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    $\begingroup$ What is the connection between the title (which focuses on $\lambda$) and the question (which appears to be only about the $\beta_j$)? I am concerned that "be optimized" could have distinctly different interpretations depending on which variables are considered the ones that can be varied and which ones are to be fixed. $\endgroup$ Commented Jan 16, 2016 at 18:18
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    $\begingroup$ thanks modified the question. I have read that the $\lambda$ is found by cross validation -- but I believe that means you have the $\beta_j$ already and use different data to find the best $\lambda$ Question is -- how do you find the $\beta_j$'s in the first place when $\lambda$ is an unknown? $\endgroup$ Commented Jan 16, 2016 at 18:29