Effect on Final State

In this set, let yt be a point representing a final state, which is either 

since the collection is convex, the final state given by 

Now for a convex set, there exists a supporting hyperplane at any boundary point of the set (see Appendix 5.B, p. 149). We apply this result to our convex set of final states, in which the final optimal state 

In light of the above facts, there exists at yf a hyperplane supporting the convex set of final states. Let 

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