where B = A−1 − 3
2EV −1EH. Obviously, if B is positive
definite, then (t) decreases monotonically by (36), implying
that it converges since (t) ≥ 0. Furthermore, when (t)
converges, it can be easily seen from (36) that '(t) converges
to some ˜ ' as t → ∞, and that w(t) = q′(t) = q(t) converges
to some w˜ (cf. (21) and (22)). Therefore ('˜,w˜) is a stationary
point of Algorithm 1 and we can take '∗ = '˜ and w∗ = w˜,
which give an optimal solution to (9). A sufficient condition
for positive definite B is provided in the following lemma
(with the proof presented in Appendix B):
where B = A−1 − 32EV −1EH. Obviously, if B is positivedefinite, then (t) decreases monotonically by (36), implyingthat it converges since (t) ≥ 0. Furthermore, when (t)converges, it can be easily seen from (36) that '(t) convergesto some ˜ ' as t → ∞, and that w(t) = q′(t) = q(t) convergesto some w˜ (cf. (21) and (22)). Therefore ('˜,w˜) is a stationarypoint of Algorithm 1 and we can take '∗ = '˜ and w∗ = w˜,which give an optimal solution to (9). A sufficient conditionfor positive definite B is provided in the following lemma(with the proof presented in Appendix B):
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