Heuristics for Optimization
Name: iterated reweighted least square

Goal: minimize function of the form $ \sum w(\theta)F(\theta)^2$, $\theta\in R^n$, $F(\theta) \in R^m$, $w(\theta)\in R$

Conditions:  depend on case

Algorithm: obvious - fix weights, solve quadratic problem, recalculate weights

Best known app: geometric median,  M-estimators,$L_p$ norm, compressed sensing

Theory:  proven on-case-to-case basis