Multiple Multipliers for Lagrangian Relaxation

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I need a small help. I apply Lagrangian Relaxation method for my optimization problem. I know how to update the multiplier via -subgradient method-when only one constraint is relaxed. However, I could not find any clear explanation for the cases when multiple constraints are relaxed and multiple multipliers exist. In such cases, how can I update the multipliers based on subgradient method?

Thank you so much