IAPG in double-loop form achieves O(ln(1/ε)/√ε) total complexity for ε-optimal solutions when ω is conic polyhedral, via quadratic growth on the dual proximal subproblem.
Zalinescu, Convex Analysis in General Vector Spaces, World Scientific, River Edge, N.J
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A Near-Optimal Total Complexity for the Inexact Accelerated Proximal Gradient Method via Quadratic Growth
IAPG in double-loop form achieves O(ln(1/ε)/√ε) total complexity for ε-optimal solutions when ω is conic polyhedral, via quadratic growth on the dual proximal subproblem.