Lagrange Multiplier Method for Variational Theory and Optimal Control and Beyond

Lagrange multipliers are a commonly employed method for the elimination of constraints in both variational theory and optimal control. However, it should be noted that the validity of this approach may be compromised when the identified multiplier is equal to zero. The paper elucidates the phenomenon of a zero multiplier and its hidden mechanism, and it proffers two methodologies for surmounting the associated challenges.