Proposes LCG method achieving O(ε^{-2} log(ε^{-1})) iteration complexity for convex functional constrained optimization and IPP-LCG with O(ε^{-3} log(ε^{-1})) for nonconvex cases, without dependence on optimal dual multiplier magnitude.
(A.1.15) In this way, we show the conclusion in ( 2.23)
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Projection-Free Functional Constrained Optimization for Risk Aversion and Sparsity Control
Proposes LCG method achieving O(ε^{-2} log(ε^{-1})) iteration complexity for convex functional constrained optimization and IPP-LCG with O(ε^{-3} log(ε^{-1})) for nonconvex cases, without dependence on optimal dual multiplier magnitude.