Complexity certifications of first order inexact Lagrangian and penalty methods for conic convex programming

摘要: In this paper we analyze first order Lagrangian and penalty methods for general cone constrained convex programming with bounded or unbounded optimal Lagrange multipliers. the part of our assume multipliers study primal-dual based on inexact information smoothing techniques (augmented Nesterov type smoothing). For (fast) gradient augmented derive overall computational complexity $\mathcal{O}\left( \frac{1}{\epsilon}\right)$ projections onto a simple primal set in to attain an $\epsilon-$optimal solution conic problem. On other hand, fast method combined technique requires \frac{1}{\epsilon^{3/2}}\right)$ same original second paper, possibly multipliers, combine strategies solving optimization We prove that, scenario, also require