A conditional-gradient single-loop augmented Lagrangian method achieves optimal convergence rates for minimizing a Lipschitz differentiable convex f plus convex h subject to smooth convex inequalities.
Bertsekas, On penalty and multiplier methods for constrained minimization
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A conditional-gradient-based single-loop augmented Lagrangian method for inequality constrained optimization
A conditional-gradient single-loop augmented Lagrangian method achieves optimal convergence rates for minimizing a Lipschitz differentiable convex f plus convex h subject to smooth convex inequalities.