Table 2.

Subgradient method parameters for solving NPER

n	iteration number
$\overline{z}$	Current best upper bound
$\underset{\_}{z}$	Current best lower bound
${\lambda }_{ih}^n,{\nu }_{j,h,h\prime }^n$	Lagrange multiplier values at iteration n
θ1, θ2	Step-size coefficient for Lagrange multipliers λih and νj,h,h′, respectively
t1, t2	Step size for the Lagrange multipliers λih and νj,h,h′, respectively
${\Gamma }_{{\lambda }_{ih}}^n,{\Gamma }_{{\nu }_{j,h,h\prime }}^n$	subgradients for the Lagrange multipliers λih and νj,h,h′, respectively, for iteration n
${\tilde{\Gamma }}_{{\lambda }_{ih}}^n,{\tilde{\Gamma }}_{{\nu }_{j,h,h\prime }}^n$	smoothed subgradients for the Lagrange multipliers λih and νj,h,h′, respectively, for iteration n
σ	minimum duality gap termination criteria
σ n	duality gap in iteration n
ζ	exponential smoothing constant
N	maximum number of iterations termination criteria