Convex optimization algorithms
Optimization and convexity

The question is now: we want to effectively minimize q of , a convex and generally non-differentiable function. It is assumed that the Lagrangian L (·, u ) admits a maximum y_u for all u. The information available is then the value q (u ) and the subgradient g_u ≥ – c (y_u ); the value y_u itself is only useful if we're also interested in solving the primal, which we isolate in § 3.3 .

In connection with remark 3, this paragraph takes the problem as it is, without seeking to adapt the methods of the differentiable case.