Optimal control in the penalty problem

As we know, for every fixed / the solution of (2.35)-(2.37) can be approximated by the solution of the following problem  

It is easily seen that the above convergence provides the passage to the lower limit in (2.62), i.e. 

On the other hand, after the passage to the limit, from (2.61) one has 

Consequently, the substitution of these values w,M in (2.63) provides the fulfilment of the inequality 

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