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the optimal value has ken reached.
The convergence of the aigorithm is proved using the following lemma and theorems.
9 t - t
Lema Let {: }Li . {: ),=, and {lV, },=, be inmite sequences. where ZI'E RI. :? E RI. und
W,'E W,C for i= 1.2. . . .. 1. where W, is closed and bounded. Suppose rhar there e-risn Q>O.
for al1 k and al1 j> k. such rhat
Pmok Recîil that. for any infinite sequence of vecton chosen h m a closed and ôounded set.
there exists at lest one convergent infinite subsequence. Therefore, there exists a convergent
infinite subsequence of {wt }y', indexed by Si Ç N. Similarly. there exists a convergent infinite