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In this paper we investigate necessary conditions of optimality forinfinite-horizon optimal control problems with overtaking optimality as anoptimality criterion. For the case of local Lipschitz continuity of the payofffunction, we construct a boundary condition on the co-state arc that isnecessary for the optimality. We also show that, under additional assumptionson the payoff function's asymptotic behavior, the Pontryagin Maximum Principlewith this condition becomes a complete system of relations, and this boundarycondition points out the unique co-state arc through a Cauchy-type formula. Anexample is given to clarify the application of this formula as an explicitexpression of the co-state arc. The cornerstone of this paper is the theorem onconvergence of subdifferentials.

On transversality condition for overtaking optimality in infinite horizon control problem