Using sequence of least squares solutions to solve non-linear problems?

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I do know about the iteratively reweighted least-squares and have played around with it to some success finding non-linear solutions (like minimizing non-2-norms to achieve solutions which seem to be more sparse). I know some optimization concepts like continuation/homotopy and suspect there could be other similar methods using sequences of linear solutions to approximate non-linear optimization problems. Does anyone have any good pointer of where to start looking?