Suppose one wants to solve the optimization question $min_{\vec{w}} f(\vec{w})$ for some lowerbounded real valued function $f$ under the constraint $c(\vec{w}) =0$.
- Given this when and how can I choose a parameter $\lambda$ s.t solving the above question would be equivalent to trying to solve $min_{\vec{w}} \left ( f(\vec{w}) + \lambda (c(\vec{w})) \right )$ ?
I was looking at lecture notes on constrained non-linear optimization, http://s3.amazonaws.com/mitsloan-php/wp-faculty/sites/30/2016/12/15031343/Optimality-Conditions-for-Constrained.pdf but nothing I see here seems to answer this question. Am I missing something?