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The method is [[Iterative method|iterative]]. At each iteration ''t'', we keep a convex region ''G<sub>t</sub>'', which surely contains the desired minimum. Initially we have ''G''<sub>0</sub> = ''G''. Then, each iteration ''t'' proceeds as follows.
* Let ''x<sub>t</sub>'' be the [[
* Compute a subgradient at ''x<sub>t</sub>'', denoted ''f''<nowiki/>'(''x<sub>t</sub>'').
** By definition of a subgradient, the graph of ''f'' is above the subgradient, so for all ''x'' in ''G''<sub>t</sub>: ''f''(''x'')−''f''(''x<sub>t</sub>'') ≥ (''x''−''x<sub>t</sub>'')<sup>T</sup>f'(''x<sub>t</sub>'').
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