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Table 1:
Comparison of Sphere Bounds.
Radius ConvergenceDynamic ScreeningReference SolutionExact Optimality of Reference
GB Can be >0 Applicable Primal Not necessary 
PGB =0a Applicable Primal Not necessary 
DGB =0 Applicable Primal/dual Not necessary 
CDGB =0 Applicable Primal/dual Not necessary 
RPB NA Not applicable Primal Necessary 
RRPB =0 Applicable Primal/dual Not necessary 
(RPB + DGB)     
Radius ConvergenceDynamic ScreeningReference SolutionExact Optimality of Reference
GB Can be >0 Applicable Primal Not necessary 
PGB =0a Applicable Primal Not necessary 
DGB =0 Applicable Primal/dual Not necessary 
CDGB =0 Applicable Primal/dual Not necessary 
RPB NA Not applicable Primal Necessary 
RRPB =0 Applicable Primal/dual Not necessary 
(RPB + DGB)     

Note: The radius convergence indicates a radius when the reference solution is the optimal solution.

aFor the hinge loss (γ=0) case, a subgradient is required to be selected appropriately for achieving this convergence.

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